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Question

The locus of points, equidistant from two intersecting lines form the _________ between the lines.

A
area
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B
angle
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C
angle bisector
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D
perpendicular bisector
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Solution

The correct option is C angle bisector

Given that two straight lines AB and CD intersecting at O. A point P is the interior of the angle AOC such that it is equidistant from AB and CD.

In the given figure,

Construct a line through O and P. Then draw PL perpendicular to AB and PM perpendicular to CD.

Consider △ POL and △ POM,

PL = PM (P is the equidistant from AB and CD)

∠PLO = ∠ PMO (Each is 90 °)

PO = PO (Common)

△ POL ≅ △ POM R.H.S

∠ POL = ∠ POM (Corresponding part of congruent triangles are congruent)

P lies on the bisector of angle AOC.


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