Class 8

Balbharti Maharashtra State Board Class 8 History Solutions Chapter 2 Europe and India Notes, Textbook Exercise Important Questions and Answers.

Maharashtra State Board Class 8 History Solutions Chapter 2 Europe and India

Class 8 History Chapter 2 Europe and India Textbook Questions and Answers

1. Rewrite the statements by choosing the appropriate options:

Question 1.
In 1453, the city of was conquered by Ottoman Turks.
(a) Venice
(b) Constantinople
(c) Rome
(d) Paris
Answer:
(b) Constantinople

Question 2.
The Industrial Revolution began in
(a) England
(b) France
(c) Italy
(d) Portugal
Answer:
(a) England

Question 3.
…….. tried to put restrictions on the illegal trade of British.
(a) Siraj-ud-Daulah
(b) Mir Kasim
(c) Mir Jafar
(d) Shah Alam
Answer:
(b) Mir Kasim

2. Explain the following concepts:

Question 1.
Colonialism:
Answer:
1. Exploitation of one country by another and making it into a colony is called Colonialism.
2. On the basis of economic and military strength one country occupies a region of another country and establishes its political supremacy.
3. Many European nations established their colonies in various parts of the continents of America, Asia, Africa and Australia.
4. They grabbed the power by using force to exploit the colonies systematically. This gave rise to Imperialism.

Question 2.
Imperialism:
Answer:

1. Imperialism means a powerful country controls other country by establishing its overall domination.
2. The objective of imperialism is to establish more and more colonies.
3. European countries with strong military power and imperialist aspirations enslaved the countries in Asia and Africa.
4. Imperialism gained momentum after industrial revolution and came to an end in twentieth century.

Question 3.
Age of Renaissance:
Answer:
(1) Renaissance literally means rebirth or revival. In the latter phase of medieval Europe, reformation, religious reform movement and geographical discoveries gained momentum.
(2) It was a comprehensive movement which touched all aspects of human life. The Greek and Roman traditions in art, architecture and philosophy were revived in the Age of Renaissance.
(3) Humanitarianism got great impetus.
(4) Renaissance inspired all round progress and ushered a new era in the history of world.
(5) This developments took place from 13th century to 16th century in Europe. This period is known as the Age of Renaissance.

Question 4.
Capitalism:
Answer:
1. Many traders participated in the competition for trade with Asia after the discovery of the new sea routes to the east.
2. As it was not possible to carry out trade single-handedly, it was decided by the traders to pool their resources to raise capital for trade.
3. Many trading companies like the East India Company were formed.
4. Trade with Oriental countries was very profitable and responsible for economic prosperity.
5. The ruling powers gave protection and trade concessions to these companies.
6. This led to the accumulation of wealth in Europe. This wealth was used as capital for trade and commerce which gave rise to capitalism in Europe.

3. Explain the following statements with reasons:

Question 1.
Siraj-ud-Daulah was defeated in the Battle of Plassey.
Answer:
1. The officers of the British East India Company misused the trade concessions and built fortification around the factory in Kolkata.
2. Siraj-ud-Daulah captured the factory at Kolkata.
3. This created discontent in England.
4. Robert Clive diplomatically bribed Mir Jafar, Commander in Chief of Nawab’s army and promised to make him Nawab of Bengal.
5. So. the Army of Siraj-ud-Daulah under the command of Mir Kasim did not join the battle against the British at Plassey in 1757 AD.
6. Thus, the British won the battle of Plassey by treachery and deceit.

Question 2.
The European countries felt the necessity of finding new sea routes to Asia.
Answer:

1. The Ottoman Turks captured Constantinople. the capital of Byzantine Empire. in 1453 AD.
2. All land trade routes joining Asia and Europe passed through this city.
3. It stopped the flow of valuable goods from the countries in the east. Therefore, the European countries felt the necessity of finding new sea routes to Asia.

Question 3.
European rulers started giving military protection and trade concessions to the trading companies.
Answer:
1. With the discovery of new sea routes to the east, trade with oriental countries became very profitable. Thus, European trade prospered.
2. Competition for trade began among many European nations.
3. The traders pooled their resources and formed trading companies like the East India Company.
4. As this trade brought economic prosperity, the European rulers started giving military protection and trade concessions to these trading companies.

4. Complete the following table.

Question 1.

Answer:

Leonardo Da Vinci :

1. A famous personality of the Renaissance period who was well versed in different branches of science and arts.
2. He had mastery over varied subjects such as sculpture, architecture, mathematics, engineering, music, astronomy, etc.
3. His paintings ‘Monalisa’ and ‘The Last Supper’ became immortal.

Let us Know:

Project:

Collect information and pictures about the work of famous painters, writers, scientists during renaissance period with the help of reference books and internet. Present a project on it in the classroom.

Class 8 History Chapter 2 Europe and India Additional Important Questions and Answers

Rewrite the statements by choosing the appropriate options:

Question 1.
American colonies organised the army under the leadership of and won against England.
(a) Thomas Jefferson
(b) Robert Clive
(c) George Washington
(d) Johannes Gutenberg
Answer:
(c) George Washington

Question 2.
The British East India Company established its factory at
(a) Kolkata
(b) Cochin
(c) Mumbai
(d) Surat
Answer:
(d) Surat

Question 3.
Siraj-ud-Daulah was defeated because diplomatically bribed Mir Jafar.
(a) Robert Clive
(b) Lord Wellesley
(c) Lord Dalhousie
(d) Lord Cornwallis
Answer:
(a) Robert Clive

Question 4.
Tipu Sultan died in the battle of in 1799.
(a) Mysore
(b) Bengaluru
(c) Srirangapatna
(d) Buxar
Answer:
(c) Srirangapatna

Question 5.
The chieftain of rose against the British.
(a) Multan
(b) Bengal
(c) Carnatic
(d) Jhansi
Answer:
(a) Multan

Question 6.
was the first Portuguese sailor who landed on the western coast of India.
(a) Christopher Columbus
(b) Bartolomeu Días
(c) Vasco-da- Gama
(d) Leonardo da Vinci
Answer:
(c) Vasco-da- Gama

Question 7.
England established colonies on the eastern coast of America.
(a) ten
(b) thirteen
(c) eight
(d) seventeen
Answer:
(b) thirteen

Name the following:

Question 1.
Invented printing press
Answer:
Johannes Gutenberg

Question 2.
Empire of Ottoman Turks
Answer:
Byzantine

Question 3.
The Bill which laid limitations on powers of the King in England.
Answer:
Bill of Rights

Question 4.
Mughal Emperor who gave permission to Britishers to establish factory at Surat.
Answer:
Emperor Jahangir

Question 5.
Came to be known as ‘World Factory’.
Answer:
England.

Answer the following in one sentence:

Question 1.
Which period in the history of Europe is known as Period of Renaissance?
Answer:
In the history of Europe, the last phase of medieval period i.e. 13th to century in Europe is known as the Period of Renaissance.

Question 2.
Name the developments that laid the foundation of modern era.
Answer:
The Renaissance, the Reformation and the geographical discoveries laid the foundation of the modern era.

Question 3.
State the significance of the invention of printing press.
Answer:
It became possible to take new ideas, new concepts and knowledge to all the sections of society due to the invention of the printing press.

Question 4.
What was the effect of the Reformation movement in the area of religion?
Answer:
Individual freedom and rationalism gained importance in the area of religion due to the Reformation movement.

Question 5.
State the principles that the French Revolution gave to the world.
Answer:
The French Revolution gave the principles of liberty equality and fraternity to the world.

Question 6.
Why did the British establish East India Company?
Answer:
The British established the East India Company to carry out trade in India.

Question 7.
What was the outcome of the American War of Independence?
Answer:
Due to American War of Independence, a new nation known as the United States of America with a federal government, written constitution and based on the principles of democracy was formed.

Do as Directed: 

1. Complete the concept Map:

Question 1.

Answer:

Question 2.

Answer:

2. Arrange the following events in chronological order on timeline:
1. Battle of Srirangapatna
2. Second Anglo-Sikh War
3. Battle of Buxar
4. Battle of Plassey
Answer:

Write short notes:

Question 1.
Leonardo-da-Vinci:
Answer:

1. Leonardo-da-Vinci is regarded as an all round personality of the Renaissance period.
2. He was well versed with the different branches of science and art.
3. He had mastery over varied subjects such as sculpture, architecture, mathematics, engineering, music, astronomy, etc.
4. But he became world-famous as a painter.
5. His paintings ‘Monalisa’ and ‘The Last Supper’ became immortal.

Question 2.
Carnatic Wars :
Answer:

1. There was competition among the European nationals to secure monopoly of trading rights in India.
2. Due to this three Cainatic wars were fought between England and France.
3. England defeated France in the third Carnatic War.
4. Alter this, there was no strong European competitor for British East India Company in India.

Question 3.
The Battle of Buxar:
Answer:

1. Mir Kasim was replaced by Mir Jafar when he tried to put restrictions on illegal practices of the British.
2. Mir Kasim, the deposed Nawab of Bengal, Shuja-ud-Daulah, the Nawab of Ayodhya and Mughal Emperor Shah Alam formed an affiance.
3. They undertook a campaign to restrain the activities of the British in Bengal.
4. They were defeated by the British in the Battle of Buxar in 1764 in Bihar.
5. The Treaty of Allahabad was signed after the Battle of Buxar. The British secured the right to collect revenue from Bengal province by this treaty.

Explain the following statements with reasons:

Question 1.
The period between 18th and 19th century came to be known as ‘Age of Revolutions’.
Answer:
1. The British Parliament passed The Bill of Rights in 1689. It established sovereignty of Parliament and curtailed powers of the King.
2. This gave momentum to the development of Parliamentary Democracy in England.
3.  The thirteen British colonies in America won the War of Independence in 1783.
4. These thirteen colonies established the first federal republic, known as the United States of America.
5. The people of France revolted against the unjust and uncontrolled monarchy and feudalism. They established a Republic.
6. The Industrial Revolution in Europe in the latter part of the 18th century brought revolutionary changes in Europe.
7. These changes had long-lasting effect on the entire world.
8. All these revolutionary events took place during 18th and 19th century period. Hence it is known as the ‘Age of Revolutions’.

Question 2.
England was described as World Factory.
Answer:

1. There were many revolutionary changes in the latter part of the 18th century in Europe.
2. Many technological innovations in Europe gave enormous outputs
3. Goods were produced with the help of machines running on steam and later on electricity. It was the dawn of the age of machines.
4. Though the industrial revolution started in England it gradually spread to other ports of the western world.
5. During this period. England enjoyed industrial prosperity and was described as World Factory.

Question 3.
The British captured Sindh in 1843.
Answer:

1. The British were afraid of Russian aggression on India via Afghanistan.
2. They decided to bring Afghanistan under their control to ensure the safety of their Indian Empire.
3. The province of Sindh was located at the Northwest frontier.
4. All routes to Afghanistan passed through Sindh.
5. Realising its strategic importance, the British captured Sindh in 1843.

Answer the following questions in 25 to 30 words:

Question 1.
Write about the Religious Reform Movement.
Answer:

1. The independent intellectuals attacked the old religious ideologies and beliefs of Roman Catholic Church.
2. The Christian priests used to give undue importance to religious rites and practices by taking advantage of the ignorance of the people.
3. They robbed people in the name of religion.
4. The movement which started against this is known as Religious Reform Movement.

Question 2.
What is Intellectual Revolution?
Answer:

1. Due to Renaissance, the European society stepped out of past ignorance and blind faith.
2. The pre-determined customs and traditions came to be seen from a critical point of view.
3. These changes are addressed as Intellectual Revolution.

Question 3.
State the significance of French Revolution.
Answer:

1. The French Revolution was the first event in world history in which the might of the people’s power was witnessed.
2. It had put an end to uncontrolled and unjust monarchy and the feudalism.
3. France became a Republican state. It gave the world principles of liberty, equality and fraternity.
4. The spread of democratic form of government began with the French Revolution.

Question 4.
What were the changes brought about by the Industrial Revolution in the system of production?
Answer:

1. The latter part of 18th century saw many technological innovations in Europe.
2. The production started with the help of machines running on steam.
3. The big factories replaced cottage industries.
4. Handlooms were replaced by machines.
5. New modes of transport like railways and steamer were available.

Question 5.
How did the conflict between Siraj- ud-Daulah and the British start?
Answer:

1. Siraj-ud-Daulah became the Nawab of Bengal in 1756.
2. The British traders misused trade concessions and fortified their factories in Kolkata without seeking permission from the Nawab.
3. So, Siraj-ud-Daulah captured the factory. This was the beginning of conflict between Siraj-ud-Daulah and the British.

Question 6.
Why were the Sikhs defeated in the First Anglo-Sikh War?
Answer:

1. Ranjitsingh, the ruler of Punjab was succeeded by his minor son Duleep Singh.
2. Queen Jindan assumed the reins of administration on behalf of her minor son.
3. Taking advantage of the inability of Queen Jindan to control the officers, the British lured some of them to their side.
4. The Sikhs attacked the British under the impression that the British would invade Punjab.
5. Thus, the Sikhs were defeated in the first Anglo-Sikh war.

Question 7.
What brought an end to the Sikh rule in Punjab in 1849?
Answer:

1. After the First Anglo-Sikh War Duleep Singh remained on throne, but the power rested in the hands of the British.
2. The Sikhs could not accept the growing impact of the British over Punjab.
3. The growing influence of the British led to the revolt by Mulraj, the chieftain of Multan.
4. Thousands of Sikh soldiers participated in this war.
5. The British defeated the Sikhs in the Second Anglo-Sikh war and annexed the whole of Punjab in 1849.

Answer the following questions in detail: (4 marks each)

Question 1.
Give detailed account of Renaissance.
Answer:
The foundation of Renaissance period was laid between 13th century and 16th century in Europe.

1. It revived the Greek and Roman traditions.
2. The changes were seen in the field of art, architecture and philosophy in Europe.
3. Humanitarianism gained great momentum.
4. There was a change in the outlook of treating each other as a human being.
5. Man became the centre of all ideologies instead of religion.
6. The sentiments and emotions of human being found expressions in the art and literature.
7. The reform movement could be found in science and different art forms.
8. Literature was produced in local languages for the better understanding of the people.
9. Renaissance was a comprehensive movement which pervaded all sectors of human life.

Question 2.
Give information about American War of Independence.
Answer:
1. After the discovery of American continent, the imperialist European powers took control of different regions of America and established their colonies.
2. England established 13 colonies on the East coast of America.
3. Initially, England kept nominal domination but later British Parliament laid oppressive restrictions and taxes on the colonies.
4. This created discontent among the people and the colonies revolted.
5. George Washington led the American army in the war against England.
6. The colonies won the war and established the first federal democratic republic, known as the United States of America.
7. USA became the first country in the world to have a written constitution and was based on the principles of Democracy.

Question 3.
What according to you are the advantages of Religious Reform Movement?
Answer:
With changing times we find changes in every field. Religious reforms are part of this process. I feel the following are the advantages of Religious Reforms Movement.

1. Superstitions give way to rational thinking.
2. Priest cannot take advantage of people’s ignorance.
3. People will not indulge in unnecessary rituals.
4. They will engage themselves in constructive work which will help them eventually.
5. Some people take advantage in the name of religion and exploit others. Religious Reforms will stop such malpractices.

Balbharti Maharashtra State Board Class 8 Maths Solutions covers the Practice Set 11.2 8th Std Maths Answers Solutions Chapter 11 Statistics.

Practice Set 11.2 8th Std Maths Answers Chapter 11 Statistics

practice set 11.2 8th class Question 1.
Observe the following graph and answer the questions.

i. State the type of the graph.
ii. How much is the savings of Vaishali in the month of April?
iii. How much is the total of savings of Saroj in the months March and April?
iv. How much more is the total savings of Savita than the total savings of Megha?
v. Whose savings in the month of April is the least?
Solution:
i. The given graph is a subdivided bar graph.
ii. Vaishali’s savings in the month of April is Rs 600.
iii. Total savings of Saroj in the months of March and April is Rs 800.
iv. Savita’s total saving = Rs 1000, Megha’s total saving = Rs 500
∴ difference in their savings = 1000 – 500 = Rs 500.
Savita’s saving is Rs 500 more than Megha.
v. Megha’s savings in the month of April is the least.

practice set 11.2 Question 2.
The number of boys and girls, in std 5 to std 8 in a Z.P. School is given in the table. Draw a subdivided bar graph to show the data. (Scale : On Y axis, 1cm = 10 students)

Standard	5th	6th	7th	8th
Boys	34	26	21	25
Girls	17	14	14	20

Solution:

Standard	5th	6th	7th	8th
Boys	34	26	21	25
Girls	17	14	14	20
Total	51	40	35	45

Statistics class 8 practice set 11.1 Question 3.
In the following table number of trees planted in the year 2016 and 2017 in four towns is given. Show the data with the help of subdivided bar graph.

Year\Town	karjat	Wadgaon	Shivapur	Khandala
2016	150	250	200	100
2017	200	300	250	150

Solution:

Year\Town	karjat	Wadgaon	Shivapur	Khandala
2016	150	250	200	100
2017	200	300	250	150
Total	350	550	450	250

Statistics class 8 Question 4.
In the following table, data of the transport means used by students in 8th standard for commutation between home and school is given. Draw a subdivided bar diagram to show the data.
(Scale: On Y axis: 1 cm = 500 students)

Means of commutation\Town	Paithan	Yeola	Shahapur
Cycle	3250	1500	1250
Bus and auto	750	500	500
On foot	1000	1000	500

Solution:

Means of commutation\Town	Paithan	Yeola	Shahapur
Cycle	3250	1500	1250
Bus and auto	750	500	500
On foot	1000	1000	500
Total	5000	3000	2250

Balbharti Maharashtra State Board Class 8 Maths Solutions covers the Practice Set 5.4 8th Std Maths Answers Solutions Chapter 5 Expansion Formulae.

Practice Set 5.4 8th Std Maths Answers Chapter 5 Expansion Formulae

Question 1.
Expand:
i. (2p + q + 5)²
ii. (m + 2n + 3r)²
iii. (3x + 4y – 5p)²
iv. (7m – 3n – 4k)²
Solution:
i. (2p + q + 5)² = (2p)² + (q)² + (5)² + 2(2p) (q) + 2(q) (5) + 2(2p) (5)
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= 4p² + q² + 25 + 4pq + 10q + 20p

ii. (m + 2n + 3r)² = (m)² + (2n)² + (3r)² + 2(m) (2n) + 2(2n) (3r) + 2(m) (3r)
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= m² + 4n² + 9r² + 4mn + 12nr + 6mr

iii. (3x + 4y – 5p)² = (3x)² + (4y)² + (- 5p)² + 2(3x) (4y) + 2(4y) (- 5p) + 2(3x) (- 5p)
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= 9x + 16y² + 25p² + 24xy – 40py – 30px

iv. (7m – 3n – 4k)² = (7m)² + (- 3n)² + (- 4k)² + 2(7m) (- 3n) + 2 (- 3n) (- 4k) + 2 (7m) (- 4k)
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= 49m² + 9n² + 16k² – 42mn + 24nk – 56km

Question 2.
Simplify:
i. (x – 2y + 3)² + (x + 2y – 3)²
ii. (3k – 4r – 2m)² – (3k + 4r – 2m)²
iii. (7a – 6b + 5c)² + (7a + 6b – 5c)²
Solution:
i. (x – 2y + 3)² + (x + 2y – 3)²
= [(x)² + (- 2y)² + (3)² + 2 (x) (- 2y) + 2 (- 2y) (3) + 2 (x) (3)] + [(x)² + (2y)² + (- 3)² + 2 (x) (2y) + 2 (2y) (- 3) + 2 (x) (- 3)]
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= x² + 4y² + 9 – 4xy – 12y + 6x + x² + 4y² + 9 + 4xy – 12y – 6x
= x + x² + 4y² + 4y² + 9 + 9 – 4xy + 4xy – 12y – 12y + 6x – 6x
= 2x² + 8y² + 18 – 24y

ii. (3k – 4r – 2m)² – (3k + 4r – 2m)²
= [(3k)² + (- 4r)² + (- 2m)² + 2 (3k) (- 4r) + 2 (- 4r) (- 2m) + 2 (3k) (- 2m)] – [(3k)² + (4r)² + (- 2m)² + 2 (3k) (4r) + 2 (4r) (- 2m) + 2 (3k) (- 2m)]
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= (9k² + 16r² + 4m² – 24kr + 16rm – 12km) – (9k² + 16r² + 4m² + 24kr – 16rm – 12km)
= 9k² + 16r² + 4m² – 24kr + 16rm – 12km – 9k² – 16r² – 4m² – 24kr + 16rm + 12km
= 9k² – 9k² + 16r² – 16r² + 4m² – 4m² – 24kr – 24kr + 16rm + 16rm – 12km + 12km
= 32rm – 48kr

iii. (7a – 6b + 5c)² + (7a + 6b – 5c)²
= [(7a)² + (- 6b)² + (5c)² + 2(7a) (-6b) + 2(-6b) (5c) + 2(7a) (5c)] + [(7a)² + (6b)² + (- 5c)² + 2 (7a) (6b) + 2 (6b) (- 5c) + 2 (7a) (- 5c)]
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= 49a² + 36b² + 25c² – 84ab – 60bc + 70ac + 49a² + 36b² + 25c² + 84ab – 60bc – 70ac
= 49a² + 49a² + 36b² + 36b² + 25c² + 25c² – 84ab + 84ab – 60bc – 60bc + 70ac – 70ac
= 98a² + 72b² + 50c² – 120bc

Maharashtra Board Class 8 Maths Chapter 5 Expansion Formulae Practice Set 5.4 Intext Questions and Activities

Question 1.
Fill in the boxes with appropriate terms in the steps of expansion. (Textbook pg. no. 27)
(2p + 3m + 4n)²
= (2p)² + (3m)² + __ + 2 × 2p × 3m + 2 × __ × 4n + 2 × 2p × __
= __ + 9m² + __ + 12pm + __ + __
Solution:
(2p + 3m + 4n)²
= (2p)² + (3m)² + (4n)² + 2 x 2p x 3m + 2 x 3m x 4n + 2 x 2p x 4n
= 4p² + 9m² + 16n² + 12pm + 24mn + 16pn

Balbharti Maharashtra State Board Class 8 Maths Solutions covers the Practice Set 2.2 8th Std Maths Answers Solutions Chapter 2 Parallel Lines and Transversals.

Practice Set 2.2 8th Std Maths Answers Chapter 2 Parallel Lines and Transversals

Question 1.
Choose the correct alternative.
i. In the given figure, if line m || line n and line p is a transversal, then find x.

(A) 135°
(B) 90°
(C) 45°
(D) 40°
Solution:
(C) 45°

Hint:

line m || line n and line p is a transversal.
∴ m∠BFG + m∠FGD = 180°
…[Interior angles]
∴ 3x + x = 180°
∴ 4x = 180°
∴ x = \(\frac { 180 }{ 4 }\)
∴ x = 45°

ii. In the given figure, if line a || line b and line l is a transversal, then find x.

(A) 90°
(B) 60°
(C) 45°
(D) 30°
Solution:
(D) 30°

Hint:

line a || line b and line l is a transversal.
∴ m∠UVS = m∠PUV
…[Alternate angles]
= 4x
m∠UVS + m∠WVS = 180°
… [Angles in a linear pair]
∴ 4x + 2x = 180°
∴ 6x = 180°
∴ x = \(\frac { 180 }{ 6 }\)
∴ x = 30°

Question 2.
In the given figure, line p || line q. Line t and line s are transversals. Find measure of ∠x and ∠y using the measures of angles given in the figure.

Solution:

i. Consider ∠z as shown in figure.
line p || line q and line t is a transversal.
∴ m∠z = 40° …(i) [Corresponding angles]
m∠x + m∠z = 180° …[Angles in a linear pair]
∴ m∠x + 40o = 180° …[From(i)]
∴ m∠x= 180° – 40°
∴ m∠x = 140°

ii. Consider ∠w as shown in the figure.
m∠w + 70° = 180° …[Angles in a linear pair]
∴ m∠w = 180° – 70°
∴ m∠w = 110° …(ii)
line p || line q and line s is a transversal.
∴ m∠y = m∠w …[Alternate angles]
∴ m∠y =110° …[From (ii)]
∴ m∠x = 140°, m∠y = 110°

Question 3.
In the given figure, line p || line q, line l || line m. Find measures of ∠a, ∠b and ∠c, using the measures of given angles. Justify your answers.

Solution:
i. line p || line q and line l is a transversal.
∴ m∠a + 80° = 180° …[Interior angles]
∴ m∠a= 180° – 80°
∴ m∠a= 100°

ii. line l || line m and line p is a transversal.
∴ m∠c = 80° …(i) [Exterior alternate angles]

iii. line p || line q and line m is a transversal.
∴ m∠b = m∠c … [Corresponding angles]
m∠b = 80° …[From (i)]
∴ m∠a = 100°, m∠b = 80°, m∠c = 80°

Question 4.
In the given figure, line a || line b, line l is a transversal. Find the measures of ∠x, ∠y, ∠z using the given information.

Solution:
line a || line b and line l is a transversal.
∴ m∠x = 105° …(i) [Corresponding angles]

ii. m∠y = m∠x … [Vertically opposite angles]
∴ m∠y = 105° …[From (i)]

iii. m∠z + 105° = 180° …[Angles in a linear pair]
∴ m∠z = 180°- 105°
∴ m∠z = 75°
∴ m∠x = 105°, m∠y = 105°, m∠z = 75°

Question 5.
In the given figure, line p || line l || line q. Find ∠x with the help of the measures given in the figure.

Solution:

line p || line l and line IJ is a transversal.
m∠IJN = m∠JIH … [Alternate angles]
∴ m∠IJN = 40° …(i)
line l || line q and line MJ is a transversal.
m∠MJN = m∠JMK … [Alternate angles]
∴ m∠MJN = 30° …(ii)
Now, m∠x = m∠IJN + m∠MJN
…[Angle addition property]
= 40° + 30° …[From (i) and (ii)]
∴ m∠x = 70°

Maharashtra Board Class 8 Maths Chapter 2 Parallel Lines and Transversals Practice Set 2.2 Intext Questions and Activities

Question 1.
When two parallel lines are intersected by a transversal eight angles are formed. If the measure of one of these eight angles is given, can we find measures of remaining seven angles? (Textbook pg, no. 9)
Solution:
Yes, we can find the measures of the remaining angles.

In the given figure, line m || line n and line l is a transversal.
m∠a = 60°(say) …(i)
i. m∠a + m∠b = 180° …[Angles in a linear pair]
∴ 60° + m∠b =180° … [From (i)]
∴ m∠b = 180° – 60°
∴ m∠b = 120° …(ii)

ii. m∠c = m∠b …[Vertically opposite angles]
∴ m∠c = 120° .. .(iii) [From (ii)]

iii. m∠d = m∠a …[Vertically opposite angles]
∴ m∠d = 60° …(iv) [From (i)]

iv. m∠e = m∠d …[Alternate angles]
∴ m∠e = 60° … [From (iv)]

v. m∠f = m∠c …[Alternate angles]
∴ m∠f = 120° …[From (iii)]

vi. m∠g = m∠d …[Corresponding angles]
∴ m∠g = 60° … [From (iv)]

vii. m∠h = m∠c … [Corresponding angles]
∴ m∠h = 120° …[From (iii)]

Question 2.
As shown in the figure (A), draw two parallel lines and their transversal on a paper. Draw a copy of the figure on another blank sheet using a trace paper, as shown in the figure (B). Colour part Land part II with different colours. Cut out the two parts with a pair of scissors. Place, part I and part II on each angle in the figure A and answer the following questions. (Textbook pg. no. 9)

1. Which angles coincide with part I?
2. Which angles coincide with part II?

Solution:

1. ∠d, ∠f and ∠h coincide with part I.
2. ∠c, ∠e and ∠g coincide with part II.

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 10 Answers Solutions Chapter 3 HCF and LCM.

HCF and LCM Class 7 Practice Set 10 Answers Solutions Chapter 3

Question 1.
Which number is neither a prime number nor a composite number?
Solution:
1

Question 2.
Which of the following are pairs of co-primes?
i. 8,14
ii. 4,5
iii. 17,19
iv. 27,15
Solution:
i. Factors of 8: 1, 2, 4, 8
Factors of 14: 1, 2, 7, 14
∴ Common factors of 8 and 14: 1,2
∴ 8 and 14 are not a pair of co-prime numbers.

ii. Factors of 4: 1, 4
Factors of 5: 1, 5
∴ Common factors of 4 and 5: 1
∴ 4 and 5 are a pair of co-prime numbers.

iii. Factors of 17: 1, 17
Factors of 19: 1, 19
∴ Common factors of 17 and 19: 1
∴ 17 and 19 are a pair of co-prime numbers.

iv. Factors of 27: 1, 3, 9, 27
Factors of 15: 1, 3, 5, 15 .
∴ Common factors of 27 and 15 : 1,3
∴ 27 and 15 are not a pair of co-prime numbers.

Question 3.
List the prime numbers from 25 to 100 and say how many they are.
Solution:
29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
There are 16 prime numbers from 25 to 100.

Question 4.
Write all the twin prime numbers from 51 to 100.
Solution:

1. 59 and 61
2. 71 and 73

Question 5.
Write 5 pairs of twin prime numbers from 1 to 50.
Solution:

1. 3,5
2. 5,7
3. 11,13
4. 17,19
5. 29,31
6. 41,43

Question 6.
Which are the even prime numbers?
Solution:
2

Maharashtra Board Class 7 Maths Chapter 3 HCF and LCM Practice Set 10 Intext Questions and Activities

Question 1.
Answer the following questions. (Textbook pg. no. 15)
i. Which is the smallest prime number?
ii. List the prime numbers from 1 to 50. How many are they?
iii. Identify the prime numbers in the list below.
17, 15 ,4, 3, 1, 2, 12, 23, 27, 35, 41, 43, 58, 51, 72, 79, 91, 97.
Solution:
i. 2 is the smallest prime number.
ii. There are 15 prime numbers from 1 to 50.
They are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
iii. [17], 15 ,4, [3], 1, [2], 12, [23], 27, 35, [41], [43], 58, 51, 72, [79], 91, [97].

Balbharti Maharashtra State Board Class 8 Maths Solutions covers the Practice Set 10.1 8th Std Maths Answers Solutions Chapter 10 Division of Polynomials.

Practice Set 10.1 8th Std Maths Answers Chapter 10 Division of Polynomials

Question 1.
Divide and write the quotient and the remainder.
i. 21m² ÷ 7m
ii. 40a³ ÷ (-10a)
iii. (- 48p⁴) ÷ (- 9p²)
iv. 40m⁵ ÷ 30m³
v. (5x³ – 3x²) ÷ x²
vi. (8p³ – 4p²) ÷ 2p²
vii. (2y³ + 4y² + 3 ) ÷ 2y²
viii. (21x⁴ – 14x² + 7x) ÷ 7x³
ix. (6x⁵ – 4x⁴ + 8x³ + 2x²) ÷ 2x²
x. (25m⁴ – 15m³ + 10m + 8) ÷ 5m³
Solution:
i. 21m² ÷ 7m

∴ Quotient = 3m
Remainder = 0

ii. 40a³ ÷ (-10a)

∴ Quotient = -4a²
Remainder = 0

iii. (- 48p⁴) ÷ (- 9p²)

∴ Quotient = \(\frac { 16 }{ 3 }\) p²
Remainder = 0

iv. 40m⁵ ÷ 30m³

∴ Quotient = \(\frac { 4 }{ 3 }\) m²
Remainder = 0

v. (5x³ – 3x²) ÷ x²

∴ Quotient = 5x – 3
Remainder = 0

vi. (8p³ – 4p²) ÷ 2p²

∴ Quotient = 4p – 2
Remainder = 0

vii. (2y³ + 4y² + 3 ) ÷ 2y²

∴ Quotient = y + 2
Remainder = 3

viii. (21x⁴ – 14x² + 7x) ÷ 7x³

∴ Quotient = 3x
Remainder = -14x² + 7x

ix. (6x⁵ – 4x⁴ + 8x³ + 2x²) ÷ 2x²

∴ Quotient = 3x³ – 2x² + 4x + 1
Remainder = 0

x. (25m⁴ – 15m³ + 10m + 8) ÷ 5m³

∴ Quotient = 5m – 3
Remainder = 10m + 8

Maharashtra Board Class 8 Maths Chapter 10 Division of Polynomials Practice Set 10.1 Intext Questions and Activities

Question 1.
Fill in the blanks in the following examples. (Textbook pg. no. 61)

1. 2a + 3a = __
2. 7b – 4b = __
3. 3p × p² = __
4. 5m² × 3m² = __
5. (2x + 5y) × \(\frac { 3 }{ x }\) = __
6. (3x² + 4y) × (2x + 3y) = __

Solution:

1. 2a + 3a = 5a
2. 7b – 4b = 3b
3. 3p × p² = 3p³
4. 5m² × 3m² = 15m⁴
5. (2x + 5y) × \(\frac { 3 }{ x }\) = \(6+\frac { 15y }{ x }\)
6. (3x² + 4y) × (2x + 3y) = 6x³ + 9x²y + 8xy + 12y²

Balbharti Maharashtra State Board Class 8 Maths Solutions covers the Practice Set 11.1 8th Std Maths Answers Solutions Chapter 11 Statistics.

Practice Set 11.1 8th Std Maths Answers Chapter 11 Statistics

Question 1.
The following table shows the number of saplings planted by 30 students. Fill in the boxes and find the average number of saplings planted by each student.

No. of saplings (Scores) xi	No. of students (frequency) fi	fi × xi
1	4	4
2	6	__
3	12	__
4	8	__
	N = __	∑ fi × xi = __

Solution:

No. of saplings (Scores) xi	No. of students (frequency) fi	fi × xi
1	4	4
2	6	12
3	12	36
4	8	32
	N = __	∑ fi × xi = 84

Question 2.
The following table shows the electricity (in units) used by 25 families of Eklara village in a month of May. Complete the table and answer the following questions.

Electricity used (Units) xi	No. of families (frequency) fi	fi × xi
30	4
45	6
60	12
75	8
90	3
	N = __	∑ fi × xi =

i. How many families use 45 units electricity?
ii. State the score, the frequency of which is 5.
iii. Find N, and ∑ f_i × x_i .
iv. Find the mean of electricity used by each family in the month of May.
Solution:

Electricity used (Units) xi	No. of families (frequency) fi	fi × xi
30	7	210
45	2	90
60	8	480
75	5	375
90	3	270
	N = 25	∑ fi × xi = 1425

i. 2 families used 45 units of electricity.
ii. The score for which the frequency is 5 is 75
iii. N = 25 and ∑ f_i × x_i = 1425
iv.

The mean of electricity used by each.

Question 3.
The number of members in the 40 families in Bhilar are as follows:
1, 6, 5, 4, 3, 2, 7, 2, 3, 4, 5, 6, 4, 6, 2, 3, 2, 1, 4, 5, 6, 7, 3, 4, 5, 2, 4, 3, 2, 3, 5, 5, 4, 6, 2,3, 5, 6, 4, 2. Prepare a frequency table and And the mean of members of 40 families.
Solution:


∴ The mean of the members of 40 families is 3.9.

Question 4.
The number of Science and Mathematics projects submitted by Model high school, Nandpur in last 20 years at the state level science exhibition is:
2, 3 ,4, 1, 2, 3, 1, 5, 4, 2, 3, 1, 3, 5, 4, 3, 2, 2, 3, 2. Prepare a frequency table and find the mean of the data.
Solution:


∴ The mean of the given data is 2.75.

Maharashtra Board Class 8 Maths Chapter 11 Statistics Practice Set 11.1 Intext Questions and Activities

Question 1.
The number of pages of a book Ninad read for five consecutive days were 60, 50, 54, 46, 50. Find the average number of pages he read everyday. (Textbook pg. no. 67)
Solution:
\(\frac{60+[50]+[54]+[46]+50}{[5]}=\frac{260}{[5]}=[52]\)
∴ Average number of pages read daily is 52

Balbharti Maharashtra State Board Class 8 Maths Solutions covers the Practice Set 9.2 8th Std Maths Answers Solutions Chapter 9 Discount and Commission.

Practice Set 9.2 8th Std Maths Answers Chapter 9 Discount and Commission

Question 1.
John sold books worth Rs 4500 for a publisher. For this he received 15% commission. Complete the following activity to find the total commission John obtained.
Solution:
Selling price of the books = Rs 4500
Rate of commission = 15%
Commission obtained = 15% of selling price
\(=\frac{[15]}{[100]} \times[4500]\)
= 15 × 45
∴ Commission obtained = 675 Rupees.
∴ The total commission obtained by John is Rs 675.

Question 2.
Rafique sold flowers worth Rs 15,000 by giving 4% commission to the agent. Find the commission he paid. Find the amount received by Rafique.
Solution:
Here, selling price of flowers = Rs 15,000,
Rate of commission = 4%
i. Commission = 4% of selling price
= \(\frac { 4 }{ 100 }\) × 15,000
= 4 x 150
∴ Commission = Rs 600

ii. Amount received by Rafique = selling price – commission
= 15,000 – 600
= Rs 14,400
∴ Rafique paid Rs 600 as commission and the amount received by him was Rs 14,400.

Question 3.
A farmer sold food grains for Rs 9200 through an agent. The rate of commission was 2%. How much amount did the agent get ?
Solution:
Here, selling price of food grains = Rs 9200,
Rate of commission = 2%
Commission = 2% of selling price
= \(\frac { 2 }{ 100 }\) × 9200
= 2 × 92
= Rs 184
∴ The agent got a commission of Rs 184.

Question 4.
Umatai purchased following items from a Khadi – Bhandar.
i. 3 sarees for Rs 560 each.
ii. 6 bottles of honey for Rs 90 each.
On the purchase, she received a rebate of 12%. How much total amount did Umatai pay?
Solution:
Here, number of sarees = 3,
Price of each saree = Rs 560
∴ Cost of 3 sarees = 560 × 3
= Rs 1680 …(i)
Also, number of honey bottles = 6,
Price of each bottle = Rs 90
∴ Cost of 6 honey bottles = 90 × 6
= Rs 540
Total amount of purchase
= cost of 3 sarees + cost of 6 honey bottles
= 1680 + 540 … [From (i) and (ii)]
= Rs 2220 …(iii)
Rate of rebate = 12%
Rebate = 12% of total amount of purchase
= \(\frac { 12 }{ 100 }\) × 2220
= 12 × 22.20
= Rs 266.40 ..(iv)
Amount paid by Umatai
= Total amount of purchase – Rebate
= 2,220 – 266.40 … [From (iii) and (iv)]
= Rs 1953.60
∴ The total amount paid by Umatai is Rs 1953.60.

Question 5.
Use the given information and fill in the boxes with suitable numbers.
Smt. Deepanjali purchased a house for Rs 7,50,000 from Smt. Leelaben through an agent. Agent has charged 2 % brokerage from both of them.
Solution:
i. Smt. Deepanjali paid 7,50,000 × \(\frac { 2 }{ 100 }\)
= 7,500 × 2 = Rs 15,000 brokerage for purchasing the house.

ii. Smt. Leelaben paid brokerage of Rs 15,000

iii. Total brokerage received by the agent is = 15,000 + 15,000 = Rs 30,000

iv. The cost of house Smt. Deepanjali paid is = 7,50,000 + 15,000 = Rs 7,65,000

v. The selling price of house for Smt.Leelaben is = 7,50,000 – 15,000
= Rs 7,35,000

Balbharti Maharashtra State Board Class 8 Maths Solutions covers the Practice Set 8.1 8th Std Maths Answers Solutions Chapter 8 Quadrilateral: Constructions and Types.

Practice Set 8.1 8th Std Maths Answers Chapter 8 Quadrilateral: Constructions and Types

Construct the following quadrilaterals of given measures.

Question 1.
In ∆MORE, l(MO) = 5.8 cm, l(OR) = 4.4 cm, m∠M = 58°, m∠O = 105°, m∠R = 90°.
Solution:

Question 2.
Construct ∆DEFG such that l(DE) = 4.5 cm, l(EF) = 6.5 cm, l(DG) = 5.5 cm, l(DF) = 7.2 cm, l(EG) = 7.8 cm.
Solution:

Question 3.
In ∆ABCD, l(AB) = 6.4 cm, l(BC) = 4.8 cm, m∠A = 70°, m∠B = 50°, m∠C = 140°.
Solution:

Question 4.
Construct ₹LMNO such that
l(LM) = l(LO) = 6 cm,
l(ON) = l(NM) = 4.5 cm, l(OM) = 7.5 cm.
Solution:

Maharashtra Board Class 8 Maths Chapter 8 Quadrilateral: Constructions and Types Practice Set 8.1 Intext Questions and Activities

Question 1.
Construction of a triangle:
Construct the triangles with given measures. (Textbook pg. no. 41)
i. ∆ABC: l(AB) = 5 cm, l(BC) = 5.5, l(AC) = 6 cm.
Solution:

Steps of construction:
Step 1 : As shown in the rough figure, draw seg BC of length 5.5 cm as the base.
Step 2 : By taking a distance of 5 cm on the compass and placing the metal tip of the compass on point B, draw an arc on one side of BC.
Step 3 : By taking a distance 6 cm on the compass and placing the metal tip of the t compass on point C and draw an arc ’ such that it intersects the previous arc. Name the point as A.
Step 4 : Draw segments AB and AC to get the triangle. ∆ABC is the required triangle.

ii. ∆DEF: m∠D = 35°, m∠F = 100°, l(DF) = 4.8 cm.
Solution:

Steps of construction:
Step 1 : As shown in the rough figure, draw seg DF of length 4.8 cm as the base.
Step 2 : Placing the centre of the protractor at point D, mark point P such that m∠PDF = 35°.
Step 3 : Placing the centre of the protractor at point F, mark point Q such that m∠QFD = 100°.
Step 4 : Draw ray DP and ray FQ. Name their point of intersection as E.
∆DEF is required triangle.

iii. ∆MNP: l(MP) = 6.2 cm, l(NP) = 4.5 cm, m∠P = 75°.
Solution:

Steps of construction:
Step 1 : As shown in the rough figure, draw seg PN of length 4.5 cm as the base.
Step 2 : Placing the centre of the protractor at point P, mark point Q such that m∠QPN = 75°.
Step 3 : By taking a distance of 6.2 cm on the compass and placing the metal tip at point P, draw an arc on ray PQ. Name the point as M.
Step 4 : Draw seg MN to get the triangle. ∆MNP is the required triangle.

iv. ∆XYZ: m∠Y = 90°, l(XY) = 4.2 cm, l(XZ) = 7 cm.
Solution:

Steps of construction:
Step 1 : As shown in the rough figure, draw seg XY of 4.2 cm as the base.
Step 2 : Placing the centre of the protractor at point Y, mark point Q such that m∠QYX = 90°.
Step 3 : By taking a distance of 7 cm on the compass and placing the metal tip on point X, draw an arc on ray YQ. Name the point as Z.
Step 4 : Draw seg XZ to get the triangle. ∆XYZ is the required triangle.

Balbharti Maharashtra State Board Class 8 Maths Solutions covers the Practice Set 8.3 8th Std Maths Answers Solutions Chapter 8 Quadrilateral: Constructions and Types.

Practice Set 8.3 8th Std Maths Answers Chapter 8 Quadrilateral: Constructions and Types

Question 1.
Measures of opposite angles of a parallelogram are (3x – 2)° and (50 – x)°. Find the measure of its each angle.
Solution:
Let ₹PQRS be the parallelogram.
m∠Q = (3x – 2)° and m∠S = (50 – x)°

m∠Q = m∠S
…..(i)
[Opposite angles of a parallelogram are congruent]
∴ 3x – 2 = 50 – x
∴ 3x + x = 50 + 2
∴ 4x = 52
∴ x = \(\frac { 52 }{ 4 }\)
∴ x = 13
Now, m∠Q = (3x – 2)°
= (3 x 13 – 2)° = (39 – 2)° = 37°
∴ m∠S = m∠Q = 37° …[From(i)]
m∠P + m∠Q = 180°
….[Adjacent angles of a parallelogram are supplementary]
∴ m∠P + 37° = 180°
∴ m∠P = 180° – 37° = 143°
∴ m∠R = m∠P = 143°
…..[Opposite angles of a parallelogram are congruent]
∴ The measures of the angles of the parallelogram are 37°, 143°, 37° and 143°.

Question 2.
Referring the given figure of a parallelogram, write the answers of questions given below.
i. If l(WZ) = 4.5 cm, then l(XY) = ?
ii. If l(YZ) = 8.2 cm, then l(XW) = ?
iii. If l(OX) = 2.5 cm, then l(OZ) = ?
iv. If l(WO) = 3.3 cm, then l(WY) = ?
v. If m∠WZY = 120°, then m∠WXY = ? and m∠XWZ = ?

Solution:
i. l(WZ) = 4.5 cm … [Given]
l(X Y) = l(WZ) ….[Opposite sides of a parallelogram are congrument ]
∴ l(X Y) = 4.5cm

ii. l(YZ) = 8.2 cm …[Given]
l(XW) = l(YZ)
…[Opposite sides of a parallelogram are congruent]
∴ l(XW) = 8.2cm … [Given]

iii. l(OX) = 2.5 cm …[Given]
l(OZ) = l(OX)
….[Diagonals of a parallelogram bisect each other]
∴ l(OZ) = 2.5cm

iv. l(WO) = 3.3 cm … [Given]
l(WO) = \(\frac { 1 }{ 2 }\) l(WY)
….[Diagonals of a parallelogram bisect each other]
∴ 3.3 = \(\frac { 1 }{ 2 }\) l(WY)
∴ 3.3 x 2 = l(WY)
∴ l(WY) = 6.6cm

v. m∠WZY =120° … [Given]
m∠WXY = m∠WZY
…..[Opposite angles of a parallelogram are congrument]
∴ m∠WXY = 120° …(i)
m∠XWZ + m∠WXY = 180°
….[Adjacent angles of a parallelogram are supplementary]
∴ m∠XWZ + 120° = 180° … [From (i)]
∴ m∠XWZ = 180°- 120°
∴ m∠XWZ = 60°

Question 3.
Construct a parallelogram ABCD such that l(BC) = 7 cm, m∠ABC = 40°, l(AB) = 3 cm
Solution:

Opposite sides of a parallelogram are congruent.
∴ l(AB) = l(CD) = 3cm
l(BC) = l(AD) = 7 cm

Question 4.
Ratio of consecutive angles of a quadrilateral is 1 : 2 : 3 : 4. Find the measure of its each angle. Write with reason, what type of a quadrilateral it is.
Solution:
Let ₹PQRS be the quadrilateral.
Ratio of consecutive angles of a quadrilateral is 1 : 2 : 3 : 4.
Let the common multiple be x.
∴m∠P = x°, m∠Q = 2x°, m∠R = 3x° and m∠S = 4x°
In ₹PQRS,
m∠P + m∠Q + m∠R + m∠S = 360°
…[Sum of the measures of the angles of a quadrilateral is 360°]
∴x° + 2x° + 3x° + 4x° = 360°
∴10 x° = 360°
∴x° = \(\frac { 360 }{ 10 }\)
∴x° = 36°
∴m∠P = x° = 36°

m∠Q = 2x° = 2 × 36° = 72°
m∠R = 3x° = 3 × 36° = 108° and
m∠S = 4x° = 4 × 36° = 144°
∴The measures of the angles of the quadrilateral are 36°, 72°, 108°, 144°.
Here, m∠P + m∠S = 36° + 144° = 180°
Since, interior angles are supplementary,
∴side PQ || side SR
m∠P + m∠Q = 36° + 72° = 108° ≠ 180°
∴side PS is not parallel to side QR.
Since, one pair of opposite sides of the given quadrilateral is parallel.
∴The given quadrilateral is a trapezium.

Question 5.
Construct ₹BARC such that
l(BA) = l(BC) = 4.2 cm, l(AC) = 6.0 cm, l(AR) = l(CR) = 5.6 cm
Solution:

Question 6.
Construct ₹PQRS, such that l(PQ) = 3.5 cm, l(QR) = 5.6 cm, l(RS) = 3.5 cm, m∠Q = 110°, m∠R = 70°. If it is given that ₹PQRS is a parallelogram, which of the given information is unnecessary?
Solution:

1. Since, the opposite sides of a parallelogram are congruent.
   ∴ Either l(PQ) or l(SR) is required.
2. To construct a parallelogram lengths of adjacent sides and measure of one angle is required.
   ∴ Either l(PQ) and m∠Q or l(SR) and m∠R is the unnecessary information given in the question.

Maharashtra Board Class 8 Maths Chapter 8 Quadrilateral: Constructions and Types Practice Set 8.3 Intext Questions and Activities

Question 1.
Draw a parallelogram PQRS. Take two rulers of different widths, place one ruler horizontally and draw lines along its edges. Now place the other ruler in slant position over the lines drawn and draw lines along its edges. We get a parallelogram. Draw the diagonals of it and name the point of intersection as T.

1. Measure the opposite angles of the parallelogram.
2. Measure the lengths of opposite sides.
3. Measure the lengths of diagonals.
4. Measure the lengths of parts of the diagonals made by point T. (Textbook pg. no. 47)

Solution:
[Students should attempt the above activities on their own.]

Question 2.
In the given figure of ₹ABCD, verify with a divider that seg AB ≅ seg CB and seg AD ≅ seg CD. Similarly measure ∠BAD and ∠BCD and verify that they are congruent. (Textbook pg. no. 48)

Solution:
[Students should attempt the above activities on their own.]