Prove the Following:

Question

Given: BR = PA, ∠IAB ≅ ∠NBP, IR ⊥ BA, and NP ⊥ AB

Prove: IR = NP

Answer 1

Triangle AIR is congruent to triangle BPN because they are right triangles with an acute angle and a leg equal.

You should show that length of AR = length of BP!

Then length of IR = length of PN because they are corresponding parts of congruent triangles.