Draw a triangle with sides 5 cm , 7 cm and 8 cm . Construct a triangle with sides of 4 5 of the corresponding sides of the first triangle.

Given: A triangle ABC , with sides 5 cm , 7 cm and 8 cm . Required: To construct a triangle similar to the triangle ABC with its sides equals to 4 5 of corresponding sides of the given triangle ABC . Steps of construction: Draw a given line segment AB = 5 cm . Draw an arc of length equals to 7 cm from point B . Draw another arc of length equals to 8 cm from point A . Consider the intersection point as C , to get the given triangle ABC . Draw a ray AX inclined to AB at an acute angle ( < 90 ° ) on the opposite side of angle C . Taking a suitable length of unit, mark 5 points P 1 , P 2 , P 3 , P 4 , P 5 on AX → , such that AP 1 = P 1 P 2 = P 2 P 3 = P 3 P 4 = P 4 P 5 = P 5 P 6 = P 6 P 7 = 1 unit Join P 5 B . From point P 4 , draw a line P 4 B ' parallel to P 5 B meeting AB produced at B ' . Draw C ' A ' parallel to CA meeting AC produced at C ' . ∴ Thus, ∆ AB ' C ' is the required triangle.

Draw a triangle ABC , in which AB = 6 cm , BC = 7 cm and ∠ B = 45 ° . Construct a triangle with sides of 5 8 of the corresponding sides of the triangle ABC .

Given: A triangle ABC , with sides AB = 6 cm , BC = 7 cm and ∠ B = 45 ° . Required: To construct a triangle similar to the triangle ABC with its sides equals to 5 8 of corresponding sides of the given triangle ABC . Steps of construction: Draw a given line segment AB = 6 cm . Draw a ray by constructing an angle ∠ B = 45 ° from point B . Draw an arc of length equals to BC = 7 cm from point B . Consider the intersection point as C and join AC , to get the given triangle ABC . Draw a ray AX inclined to AB at an acute angle ( < 90 ° ) on the opposite side of angle C . Taking a suitable length of unit, mark 8 points P 1 , P 2 , P 3 , P 4 , P 5 , P 6 , P 7 , P 8 on AX → , such that AP 1 = P 1 P 2 = P 2 P 3 = P 3 P 4 = P 4 P 5 = P 5 P 6 = P 6 P 7 = P 7 P 8 = 1 unit Join P 8 B . From point P 5 , draw a line P 5 B ' parallel to P 8 B meeting AB produced at B ' . Draw C ' A ' parallel to CA meeting AC produced at C ' . ∴ Thus, ∆ AB ' C ' is the required triangle.

Construct a triangle ABC , in which BC = 5 cm and ∠ B = 60 ° and AB + AC = 8 cm . Construct a triangle with sides of 5 4 of the corresponding sides of the triangle ABC .

Given: A triangle ABC , with sides AB + AC = 8 cm , BC = 5 cm and ∠ B = 60 ° . Draw the base BC and at the point B make an angle 60 ° . Cut a line segment BD equal to AB + AC from the ray BX. Join DC and make an angle DCY equal to BDC. To construct a triangle similar to the triangle ABC with its sides equals to 5 4 of corresponding sides of the given triangle ABC . Steps of construction: Draw a given line segment BC = 5 cm . Draw a ray by constructing an angle ∠ B = 60 ° from point B . Consider the intersection point as A and join AC , to get the given triangle ABC . Draw a ray BX inclined to BC at an acute angle ( < 90 ° ) on the opposite side of angle A . Taking a suitable length of unit, mark 5 points P 1 , P 2 , P 3 , P 4 , P 5 on B X → , such that B P 1 = P 1 P 2 = P 2 P 3 = P 3 P 4 = P 4 P 5 = 1 unit Join P 5 C . From point P 4 , draw a line P 4 C ' parallel to P 5 C meeting B C produced at C ' . Draw C ' A ' parallel to CA meeting AC produced at C ' . ∴ Thus, ∆ A ' B C ' is the required triangle.

E M B I B E

Mathematics for Class 10>Chapter 9 - Construction>EXERCISE 9.1

Manipur Board Solutions for Chapter: Construction, Exercise 1: EXERCISE 9.1

Author:Manipur Board

Manipur Board Mathematics Solutions for Exercise - Manipur Board Solutions for Chapter: Construction, Exercise 1: EXERCISE 9.1

Attempt the practice questions on Chapter 9: Construction, Exercise 1: EXERCISE 9.1 with hints and solutions to strengthen your understanding. Mathematics for Class 10 solutions are prepared by Experienced Embibe Experts.

Questions from Manipur Board Solutions for Chapter: Construction, Exercise 1: EXERCISE 9.1 with Hints & Solutions

MEDIUM

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 9 - Construction>EXERCISE 9.1>Q 1

Draw any line and divide it in the ratio $3 : 8$ .

MEDIUM

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 9 - Construction>EXERCISE 9.1>Q 1

Draw any line and divide it in the ratio $4 : 9$ .

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 9 - Construction>EXERCISE 9.1>Q 2

Draw any line segment of $8.7 cm$ and divide it in the ratio $5 : 9$ . Measure the two parts.

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 9 - Construction>EXERCISE 9.1>Q 3

Construct a right triangle with sides $3 cm, 4 cm and 5 cm$ . And then construct a triangle similar to the right triangle, the scale factor being $\frac{7}{4}$ .

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 9 - Construction>EXERCISE 9.1>Q 4

Draw a triangle with sides $5 cm, 7 cm and 8 cm$ . Construct a triangle with sides of $\frac{4}{5}$ of the corresponding sides of the first triangle.

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 9 - Construction>EXERCISE 9.1>Q 5

Draw a triangle $ABC$ , in which $AB = 6 cm, BC = 7 cm$ and $∠ B = 45 °$ . Construct a triangle with sides of $\frac{5}{8}$ of the corresponding sides of the triangle $ABC$ .

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 9 - Construction>EXERCISE 9.1>Q 6

Construct a triangle $ABC$ , in which $BC = 5 cm$ and $∠ B = 60 °$ and $AB + AC = 8 cm$ . Construct a triangle with sides of $\frac{5}{4}$ of the corresponding sides of the triangle $ABC$ .

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 9 - Construction>EXERCISE 9.1>Q 7

Construct an isosceles triangle of a base and altitude. Then construct another triangle whose sides are $\frac{3}{2}$ times the corresponding sides of the first triangle.

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