Question

Given: Base ∡BAC and ∡ACB are congruent.

Prove: ∆ABC is an isosceles triangle.

When completed, the following paragraph proves that segment AB is congruent to segment BC making ∆ABC an isosceles triangle.

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

Answer 1

(rest of question) Segment AD
is congruent to Segment DC by _______1________.
∆BAD is congruent to ∆BCD by the _______2________.
Segment AB is congruent to Segment BC because corresponding parts of congruent triangles are congruent (CPCTC).
Consequently, ∆ABC is isosceles by definition of an isosceles triangle.