# n the given figure PQRS is a parallelogram and the line segments PA and RB bisect the angles P and R respectively. Show that PA || RB

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by remyyazz

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by remyyazz

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.`. ∠R = 2x degrees (as opp angles of a parallelogram are equal)

.`. ∠APB = ∠ ARB = 2x/2 = x degrees (as PA and RB bisects ∠P and ∠ R respectively [given])

A line segment PQ is drawn through the points P and Q such that it bisects the angles ∠APB and ∠ARB.

Let PQ be a transversal.

Alternate angles ∠PRB and ∠APR are formed.

∠PRB = ∠ APR = x /2 degrees (as PQ bisects angles ∠APB and ∠ARB)

.`. Alternate angles are equal.

.`. PA || RB [Proved]

In quardilateral PARB

1/2

angle BPR = angle BRA (PA &RB are angle bisectors)

PQllSR

so PBllAR

therefore PBRS is a llgm with opposite side equal and opposite side equal

so PAllRB (opposite sides of a llgm are equal )