In ∆ABC shown below, ∡BAC is congruent to ∡BCA.
Given: Base ∡BAC and ∡ACB are congruent.

Prove: ∆ABC is an isosceles triangle.

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

Construct a perpendicular bisector from point B to .
Label the point of intersection between this perpendicular bisector and as point D.
m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector.
∡BDA is congruent to ∡BDC by the _______1________.
is congruent to by _______2________.
∆BAD is congruent to ∆BCD by the Angle-Side-Angle

Question

In ∆ABC shown below, ∡BAC is congruent to ∡BCA.
Given: Base ∡BAC and ∡ACB are congruent.

Prove: ∆ABC is an isosceles triangle.

When completed, the following paragraph proves that  is congruent to  making ∆ABC an isosceles triangle.

Construct a perpendicular bisector from point B to . 
Label the point of intersection between this perpendicular bisector and  as point D. 
m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector. 
∡BDA is congruent to ∡BDC by the _______1________. 
 is congruent to  by _______2________. 
∆BAD is congruent to ∆BCD by the Angle-Side-Angle