Question

Given: PQR and PSR are right triangles, PR bisects QPS Prove: PQR=PSR You may use either a two column proof or paragraph proof.

Answer 1

The two triangles are congurent based on the relationship of side angle side (SAS)

Here, we want to prove that the two triangles are congruent.

Since the line PR bisects the angle QPS, we can have two deductions here;

1. The line PR divides te line QS into teo equal halves

2. There is an equal measure of angle on both triangles at the vertice P

Thus, factoring this into consideration, we can have the triangles with the following marked points;

Kindly note that the side PR is common to both triangles

So we have two equal sides and an equal angle

So the relationship of congruency between the two triangles is side angle side which can be written as SAS

Thus we have proven that both triangles are congruent