Question

If P is a point equidistant from two lines l and m intersecting at point A show that line AP bisects the angle between them.

Answer 1

Answer:

Step-by-step explanation:

Hi,

Given 2 lines l and m intersecting at point A.

Given that P is equidistant from the given two lines.

Let the foot of the perpendicular onto the line l be M.

Let the foot of the perpendicular onto the line m be N.

Given that PM = PN

Consider Δ APM and Δ APN, then we have

AP = AP (common side)

PM = PN (Given)

∠PMA = ∠PNA = 90°

Hence , by R.H.S congruency both the triangle are congruent

Δ APM ≅  Δ APN

Hence , angles opposite to equal sides would be equal.

Thus, ∠PAM = ∠PAN

Hence, AP is the angular bisector of lines l and m.

Hope, it helps !

Answer 2

hope this will help you