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 definition of congruent angles.
is congruent to by by the definition of a perpendicular bisector.

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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 definition of congruent angles. 
 is congruent to  by by the definition of a perpendicular bisector. 

∆