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:

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.

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Answer 2

Step-by-step explanation:

SEE THE ATTACHMENT..

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