Q. 314.2( 6 Votes )

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


Answer :

Given: P is a point in the interior of AOB and PL OA and PM OB such that PL=PM


To prove: POL = POM


Proof:


In ∆OPL and ∆OPM, we have


OPM = OPL = 90° …given


OP = OP …common side


PL = PM … given


Thus by Right angle hypotenuse side property of congruence,


∆OPL OPM


Hence, we know that, corresponding parts of the congruent triangles are equal


POL = POM


Ie. OP is the bisector of AOB


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