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.

Answer 1

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 (ASA) Postulate.
is congruent to because corresponding parts of congruent triangles are congruent (CPCTC).
Consequently, ∆ABC is isosceles by definition of an isosceles triangle.

1. the definition of congruent angles
2. Angle-Side-Angle (ASA) Postulate

1. the definition of congruent angles
2. the definition of a perpendicular bisector

1. Angle-Side-Angle (ASA) Postulate
2. the definition of a perpendicular bisector

1. Angle-Side-Angle (ASA) Postulate
2. corresponding parts of congruent triangles are congruent (CPCTC)

Answer 2

@ganeshie8

Answer 3

draw a perpendicular bisector from B to AC