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