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  • Two lines l and m intersect at the point O and P is a point on a line n passing through the point O such that P is equidistant from l and m. Prove that n is the bisector of the angle formed by l and m.

Two lines l and m intersect at the point O and P is a point on a line n passing through the point O such that P is equidistant from l and m. Prove that n is the bisector of the angle formed by l and m.

Answers (1)

Given: l and m intersect at point O and P is a point on a line n passing through O and

PQ = PR

To prove: \angleQOP = \angleROP

Proof: In \trianglePOR and \trianglePOQ

PQ = PR                                              (Given)

\anglePQO = \anglePRO = 90°             (P is equidistant from l and m)

So PQ and PR should be perpendicular to lines l and m respectively

\therefore \trianglePOR \cong\trianglePOQ                    (by RHS congruence)

\angleROP = \angleQOP                                   (by CPCT)

Hence Proved.

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