Question

Given triangle ABC with angle ABC congruent to angle ACB, which step could be used to prove that side AB is congruent to side AC?

A) Construct a midpoint on segment AB
B) Construct a midpoint on segment BC
C) Construct a bisector of angle BAC
D) Construct a bisector of angle ABC

Answer 1

An appropriate step is ...
C) Construct a bisector of angle BAC

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I suppose you could get there faster by claiming ΔABC ≅ ΔACB by ASA, then AB ≅ AC by CPCTC.