Question

p is a point equidistant from two lines L and M intersect at point A.show that AP bisect the angle between them.​

Answer 1

Step-by-step explanation:

You are given that lines l and m intersect each other at A.

Let PB is perpendicular on l and

PC⊥m. It is given that PB=PC.

You need to show that ∠PAB=∠PAC.

Let us consider △PAB and △PAC. In these two triangles,

PB=PC (Given)

∠PBA=∠PCA=90∘ (Given)

PA=PA (Common side)

So, △PAB≅△PAC (RHS rule)

So, ∠PAB=∠PAC(CPCT)