Question

In ΔABC shown below, ∠BAC is congruent to ∠BCA:

Answer 1

Construct a perpendicular bisector from point B to Line segment AC.
Label the point of intersection between this perpendicular bisector and Line segment AC as point D:

m∠BDA and m∠BDC is 90° by the definition of a perpendicular bisector.

∠BDA is congruent to ∠BDC by the definition of congruent angles.

Line segment AD is congruent to Line segment DC by the definition of a perpendicular bisector.

ΔBAD is congruent to ΔBCD by the Angle-Side-Angle (ASA) Postulate.

Line segment AB is congruent to Line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).

Consequently, ΔABC is isosceles by definition of an isosceles triangle.

Therefore, the correct answer is C.