Question

PQRS is a parallelogram and the bisect or of angle P bisects QR at M .show that PS=2PQ

Answer 1

Proved below.

Step-by-step explanation:

Given:

Here PQRS is a parallelogram and PM bisects QR

So, QM = MR                                   (1)

also, PM bisects angle P

∠ SPM = ∠ MPQ               (2)

Now, PS || QR and PM is transversal

so,  ∠ SPM =  ∠ PMQ  (alternate interior angles)             (3)

from (2) and (3)

∠ MPQ = ∠ PMQ

so, QM = PQ (sides opposite to equal angles are equal in a triangle)    (4)

From (1) and (4)

PQ = QM = MR

Now, QM + MR = QR

QR = PQ + PQ           ( since PQ = QM = MR)

or, QR = 2(PQ)

Also, QR = PS            (Opposite sides of a parallelogram are equal)

So, PS = 2 PQ

Hence proved.

Answer 2

Answer:

check the below explaination

Step-by-step explanation:

shown down