It is given that ∠abr and ∠acr are right angles, ab ≅ bc and bc ≅ ac since they contain right angles, △abr and △acr are right triangles. the right triangles share hypotenuse ar, and reflexive property justifies that ar ≅ ar. since ab ≅ bc and bc ≅ ac, the transitive property justifies ab ≅ ac. now, the hypotenuse and leg of right △abr is congruent to the hypotenuse and the leg of right △acr, so △abr ≅ △acr by the hl congruence postulate. therefore, by cpctc, and bisects ∠bac by the definition of bisector.