Question

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

• A. area
• B. angle
• C. angle bisector
• D. perpendicular bisector

Answer 1

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

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

$\therefore$ P lies on the bisector of angle AOC.