# 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.

##### 1 Answer

Nov 19, 2015

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).