Question

In the adjoining figure, P is a point in the interior of angle AOB. if PL perdicular OA and PM perdicular OB such that PL=PM,show that OP is the bisector of angle AOB.​

Answer 1

In the above Question , the following information is given -

In the adjoining figure, P is a point in the interior of angle AOB.

PL is perpendicular OA and PM is perpendicular OB such that PL= PM .

To show -

OP is the bisector of angle AOB.​

Solution -

We can say that OP is the bisector of angle AOB if and only if triangle OPL is congruent to triangle OPM .

So , we need to prove that triangle OPL is congruent to triangle OPM .

Now , -

PL is perpendicular OA and PM is perpendicular OB such that PL= PM .

So ,

Angle OLP = Angle OMP ......... { 1 }

PL = PM .......... {2}

OP = OP ......... { 3 }

So , triangle OLP is congruent to triangle OMP by R. H. S congruency .

So ,

Angle LOP = Angle POM { Corresponding parts of congruent triangles }

So , we can say that -

OP is the bisector of angle AOB.​

Hence Shown .....

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Answer 2

Step-by-step explanation:

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