Question

in the figure line ab parallel line CD and line PR is there transversal if we draw angle bisector of both pairs of alternative angles then □ PQRS is formed name the type of □ PQRS​

Answer 1

Answer:

First of All , Hope your Maharashtra Scholarship Exam went well. The answer is (a)right angled quailateral

Step-by-step explanation:

Given: PR is transversal of parallel line AB and line CD.

∠ APR + ∠ CRP = 180°

(divide by 2)

∠ SPR + ∠ SRP = 90°

[ PS and RS are bisector)

In Δ PRS

∠ SPR + ∠ SRP + ∠ RSP = 180°

90° + ∠ PSR = 180° (∠ SPR  + ∠ SRP = 180° proved above)

∠ PSR = 180° -90°

∠ PSR = 90°

Similarly, ∠ QPR = 90°

∠ APR + ∠ BPR = 180 (straight line)

(divide by 2)

∠ SPR + ∠ QPR = 90° (PS and PQ are bisector ∠)

∠ SPQ = 90°

Similarly, ∠ SRQ = 90°

By using similarity of triangles we can prove that SP ≅  SQ

If any quadrilateral has all the angle 90° it is a rectangle, so that QPQRS is rectangle.

Thanks!