Construct a quadrilateral, similar to a given quadrilateral A B C D with its sides 4 5 th of the corresponding sides of A B C D . Also, write the steps of construction.

Given that, a quadrilateral A B C D and scale factor = 4 5 . We have to construct a quadrilateral A B C D and a similar quadrilateral A B ' C ' D ' , in which each side of A B ' C ' D ' is 4 5 th of corresponding sides of A B C D . Step of construction: Step 1 . Draw a quadrilateral A B C D . Step 2 . Join A C and draw any ray A X inclined at a certain angle with A C such that ∠ B A X is an acute angle. Step 3 . Along A X , mark 5 points A 1 , A 2 , A 3 , A 4 and A 5 such that A A 1 = A 1 A 2 = A 2 A 3 = A 3 A 4 = A 4 A 5 . Step 4 . Join A 5 C . Step 5 . From A 4 , draw A 4 C ' parallel to A 5 C (draw an angle equal to ∠ A A 5 C ), to intersect A C at C ' . Step 6 . From C ' , draw C ' D ' parallel to C D (draw an angle equal to ∠ A C D ), to intersect A D at D ' . Step 7 . From C ' , draw C ' B ' parallel to C B (draw an angle equal to ∠ A C B ), to intersect A B at B ' . Then A B ' C ' D ' is the required quadrilateral whose sides are 4 5 th of the corresponding sides of the quadrilateral A B C D .

Draw a △ A B C with side B C = 6 cm , ∠ B = 30 ° and ∠ A = 120 ° . Then construct a triangle whose sides are 3 4 times the corresponding sides of △ A B C .

Given that, B C = 6 cm , ∠ B = 30 ° , ∠ A = 120 ° , so ∠ C = 180 ° - 120 ° + 30 ° = 180 ° - 150 ° = 30 ° 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 = 6 cm . Step 2 . At B draw an angle ∠ P B C = 30 ° . Step 3 . At C draw an angle ∠ Q C B = 30 ° . Step 4 . P B and Q C intersects at A . 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 . Thus, △ 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 11

HARD

10th CBSE

IMPORTANT

Earn 100

Draw a pair of tangents to a circle of radius $5 cm$ which are inclined to each other at an angle of $60 °$ .

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 9

Construct a quadrilateral, similar to a given quadrilateral

A B C D

with its sides

\frac{4}{5} th

of the corresponding sides of

A B C D

. Also, write the steps of construction.

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 11 - Constructions>EXERCISE>Q 10

Construct a quadrilateral $A B C D$ , in which $A B = 1.2 cm, B C = 1.8 cm, C D = 1.8 cm, A C = 1.8 cm$ and $A D = 1.3 cm$ . Construct another quadrilateral $A B' C' D'$ , with diagonal $A C' = 3 cm$ , such that it is similar to quadrilateral $A B C D$ .