Question

PQRS. Is a parallelogram and the bisector of angle p bisects QR at m.show PS=2pq

Answer 1

Step-by-step explanation:

Given: PQRS is a parallelogram.

M is the midpoint of QR and PM bisects angle P.

• To prove: PS=2PQ

• Proof: PQRS is a parallelogram so, PS//RQ

angle SPM=angle PMQ_(i) (Alternate interior angle)

• angle SPM=angleMPQ_(ii) (Given)

• From (i) and (ii),

angle PMQ=angle MPQ

Therefore, PQ=QM

• PQ=1/2 RQ (M is midpoint of QR)

PQ=1/2 PS (Opposite sides of parallelogram are equal)

2PQ=PS

PS=2PQ