Question

Pqrs is a parallelelogram, PO &qo are the bisector of angle p&angle q respectively. Prove that poq=90
degree

Answer 1

Given:

1. PQRS is a parallelogram where the opposite sides are parallel and equal .

2. PO & QO are the angle bisector of angle P and Q respectively.

To prove that:

Angle POQ is 90°

Step-by-step explanation:

Proof:

In parallelogram PQRS

Angle P + angle Q = 180°

(Co-interior angle)

1/2 angle P + 1/2 angle Q = 180°/2 = 90°

From 2 we get:

Angle OPQ + angle OQP = 90°.................(i)

In triangle OPQ,

Angle (OPQ + OQP + POQ) = 180°.............(ii)

(Angle sum property)

From (i)and(ii) , we get:

Angle POQ = 180° - Angle( OPQ + OQP)

= 180° - 90° = 90°

Hence Proved.