Construct a triangle similar to a given triangle A B C with its sides equal to 3 4 of the corresponding sides of the triangle A B C (i.e. of scale factor 3 4 ).

Given that, scale factor = 3 4 To construct a triangle A B C and a similar triangle A ' B C ' , in which each side of △ A ' B C ' is 3 4 th of corresponding sides of △ A B C . Step of construction: Step 1 . Draw a △ A B C . Step 2 . On B draw an acute angle ∠ C B X downwards. Step 3 . Along B X , mark 4 points B 1 , B 2 , B 3 and B 4 such that B B 1 = B 1 B 2 = B 2 B 3 = B 3 B 4 . Step 4 . Join B 4 C . Step 5 . From B 3 , draw B 3 C ' parallel to B 4 C (draw an angle equal to ∠ B B 4 C ), meeting B C in C ' , such that B C ' is 3 4 of B C . Step 6 . From C ' , draw A ' C ' parallel to A C (draw an angle equal to ∠ A C B ), meeting A B in A ' , such that A ' B is 3 4 of A B . Then △ A ' B C ' is the required triangle whose sides are 3 4 th of the corresponding sides of the △ A B C .

Draw a triangle A B C with side B C = 3 . 5 cm , A B = 3 . 5 cm and ∠ A B C = 60 ∘ . Then construct a triangle whose sides are 3 4 of the corresponding sides of the triangle A B C .

Given that, B C = 3 . 5 cm , A B = 3 . 5 cm , ∠ A B C = 60 ∘ and scale factor = 3 4 . We have to construct a triangle A B C and a similar triangle A ' B C ' , in which each side of △ A ' B C ' is 3 4 th of corresponding sides of △ A B C . Step of construction: Step 1 . Take B C = 3 . 5 cm . Step 2 . At B draw an angle ∠ P B C = 60 ∘ . Step 3 . From point B draw an arc of 3 . 5 cm , intersecting the ray B P at A . Step 4 . Join A C . Then A B C is the required triangle. Step 5 . On B draw an acute angle ∠ C B X downwards. Step 6 . Along B X , mark 4 points B 1 , B 2 , B 3 and B 4 such that B B 1 = B 1 B 2 = B 2 B 3 = B 3 B 4 . Step 7 . Join B 4 C . Step 8 . From B 3 , draw B 3 C ' parallel to B 4 C (draw an angle equal to ∠ B B 4 C ), meeting B C in C ' , such that B C ' is 3 4 of B C . Step 9 . From C ' , draw A ' C ' parallel to A C (draw an angle equal to ∠ A C B ), meeting A B in A ' , such that A ' B is 3 4 of A B . Then △ A ' B C ' is the required triangle whose sides are 3 4 th of the corresponding sides of the △ A B C .

Construct a triangle with sides 2 . 4 cm , 1 . 8 cm and 2 . 1 cm and then construct a triangle whose sides are 3 4 of the corresponding sides of the first triangle.

Given that, the three sides of a triangle are 2 . 4 cm , 1 . 8 cm , 2 . 1 cm and scale factor = 3 4 . We have to construct a triangle A B C and a similar triangle A ' B C ' , in which each side of △ A ' B C ' is 3 4 th of corresponding sides of △ A B C . Step of construction: Step 1 . Take B C = 2 . 4 cm . Step 2 . From point B draw an arc of 2 . 1 cm and from point C draw an arc of 1 . 8 cm , cutting each other at point A . Step 3 . Join A B and A C . Then A B C is the required triangle. Step 4 . On B draw an acute angle ∠ C B X downwards. Step 5 . Along B X , mark 4 points B 1 , B 2 , B 3 and B 4 such that B B 1 = B 1 B 2 = B 2 B 3 = B 3 B 4 . Step 6 . Join B 4 C . Step 7 . From B 3 , draw B 3 C ' parallel to B 4 C (draw an angle equal to ∠ B B 4 C ), meeting B C in C ' , such that B C ' is 3 4 of B C . Step 8 . From C ' , draw A ' C ' parallel to A C (draw an angle equal to ∠ A C B ), meeting A B in A ' , such that A ' B is 3 4 of A B . Then △ A ' B C ' is the required triangle whose sides are 3 4 th of the corresponding sides of the △ A B C .

E M B I B E

New Mathematics for Class X>Chapter 11 - Constructions>REVISION EXERCISE>Q 14

HARD

10th CBSE

IMPORTANT

Earn 100

Draw a pair of tangents to a circle of radius $3.5 cm$ which are perpendicular to each other.

Important Questions on Constructions

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 11 - Constructions>EXERCISE>Q 4

Draw a line segment of length

3.5 cm

and divide it externally in the ratio

7 : 3

. Measure the two parts.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 11 - Constructions>EXERCISE>Q 1

Construct a triangle similar to a given triangle

A B C

with its sides equal to

\frac{3}{4}

of the corresponding sides of the triangle

A B C

(i.e. of scale factor

\frac{3}{4}

).

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 11 - Constructions>EXERCISE>Q 3

Draw a triangle

A B C

with side

B C = 3.5 cm, A B = 3.5 cm

and

∠ A B C = 60^{\circ}

. Then construct a triangle whose sides are

\frac{3}{4}

of the corresponding sides of the triangle

A B C

.

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 11 - Constructions>EXERCISE>Q 4

Construct a triangle with sides

2.4 cm, 1.8 cm

and

2.1 cm

and then construct a triangle whose sides are

\frac{3}{4}

of the corresponding sides of the first triangle.

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 11 - Constructions>EXERCISE>Q 5

Construct a triangle

A Q C

similar to a given triangle

P Q R

with

Q R = 3 cm, P Q = 2 cm, P R = 2.6 cm

such that each of its is

3 / 4 th

of the corresponding sides of

△ P Q R

.

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 11 - Constructions>EXERCISE>Q 6

Construct a triangle

A Q C

similar to a given triangle

P Q R

with

Q R = 4.5 cm

,

P Q = 3.1 cm

,

P R = 3.3 cm

such that each of its is

5 / 7 th

of the corresponding sides of

△ P Q R

.

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 11 - Constructions>EXERCISE>Q 7

Construct a triangle

P B C

similar to a given equilateral triangle

P Q R

with sides

3.5 cm

, such that each of its is

6 / 7 th

of the corresponding sides of

△ P Q R

.

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 11 - Constructions>EXERCISE>Q 8

Construct a triangle $A Q C$ similar to a given equilateral triangle $P Q R$ with sides $3 cm$ , such that each of its is $\frac{3}{4} th$ of the corresponding sides of $△ P Q R$ . Also, draw a circumcircle of $△ A Q C$ . [Do not write the steps of construction].