Okay so 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, ∠BAR ≅ ∠CAR by CPCTC, and bisects ∠BAC by the definition of bisector.
