Question

33. In fig. line AB || line CD and line PR is their transversal. If we draw angle bisector of
both pairs of alternative angle then PQRS is formed, Name the type of PQRS.
40
(1) Right angle quadrilateral
P/
B
(2) Kite
1) Square
(4) Trapezium​

Answer 1

PQRS will be a right angle quadrilateral.

Step-by-step explanation:

See the attached diagram.

Given that, ∠ RPS = 1/2 ∠ APR = 1/2 ∠ PRD = ∠ PRQ

And, ∠ QRP = 1/2 ∠ RPB = 1/2 ∠ PRC = ∠ PRS

So, ∠ SPQ = ∠ SPR + ∠ QPR = 1/2 ∠ APR + 1/2 ∠ RPB = 1/2(180°) = 90°

Similarly, ∠ SRQ = ∠ SRP + ∠ QRP = 1/2 ∠ CRP + 1/2 ∠ PRD = 1/2(180°) = 90°.

Now, ∠ SRP + ∠ RPS = 1/2 ∠ CRP + 1/2 ∠ APR = 1/2(180°) = 90°

So, ∠ RSP = 180° - (∠ SRP + ∠ RPS) = 180° - 90° = 90°

Again, ∠ PRQ + ∠ QPR = 1/2 ∠ PRD + 1/2 ∠ RPB = 1/2(180°) = 90°

So, ∠ RQP = 180° - (∠ PRQ + ∠ QPR) = 180° - 90° = 90°.

We can not say anything about the sides of PQRS.

So, PQRS will be a right angle quadrilateral. (Answer)