Question

Given: Base ∡BAC and ∡ACB are congruent.

Prove: ∆ABC is an isosceles triangle.

Answer 1

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.

∆BAD is congruent to ∆BCD by the _______1________.
is congruent to because _______2________.
Consequently, ∆ABC is isosceles by definition of an isosceles triangle.

1. corresponding parts of congruent triangles are congruent (CPCTC)
2. the definition of a perpendicular bisector

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

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

1. the definition of congruent angles
2. corresponding parts of congruent triangles are congruent (CPCTC)

Answer 2

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