Question

In the given figure, P is a point in the interior of ∠ AOB. If PL is perpendicular to OA
and PM is perpendicular to OB such that PL = PM, show that OP is the bisector of ∠ AOB

Answer 1

Answer:

In the given figure, P is a point in the interior of ∠ AOB. If PL is perpendicular to OA

and PM is perpendicular to OB such that PL = PM, show that OP is the bisector of ∠ AOB

Answer 2

Step-by-step explanation:

GIVEN,, angle PLO = 90°

angle PMO = 90°.

PL=PM.

PO IS A COMMON SIDE OF BOTH ∆PLO & ∆PMO. SO,, PO=PO.

IN ∆PLO & ∆PMO,,

1. ANGLE PMO = ANGLE PLO (both of them are 90°)

2. PM = PL (GIVEN).

3. PO = PO (COMMON SIDE).

SO, ∆PLO IS CONGRUENT TO ∆PMO.

( BY RHS CONGRUENCE).

THEREFORE,, ANGLE POM = ANGLE POL

(BY C P C T).

THEREFORE,, OP IS THE BISECTOR OF ANGLE AOB. HENCE PROVED!!..

HOPE IT WILL BE HELPFUL!!