Question

How would I prove that if the base angles of a triangle are congruent, then the triangle is isosceles? Please provide a two column proof.

Answer 1

Because Congruent angles can be used to prove and Isosceles Triangle congruent to itself.

Explanation:

First draw a Triangle with the to-be base angles as < B and < C and vertex < A.*

Given: < B congruent < C

Prove: Triangle ABC is Isosceles.

Statements:

1. < B congruent < C
2. Segment BC congruent Segment BC
3. Triangle ABC congruent Triangle ACB
4. Segment AB congruent Segment AC

Reasons:

1. Given
2. By Reflexive Property
3. Angle Side Angle (Steps 1, 2, 1)
4. Congruent Parts of Congruent Triangles are Congruent.

And since we now know the Legs are congruent we can truly state that the triangle is isosceles by proving it congruent to the mirror of itself.

*Note: < (Letter) means Angle (Letter).