Question

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

Answer 1

Let ∠P = 2x degrees
.`. ∠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]

Answer 2

Answer:

Step-by-step explanation:

Let ∠P = 2x degree

=>∠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]