In Exercises 25 and 26, complete each proof shown on page 160.
Given:  Equilateral

Prove: 

PROOF  
Statements  Reasons 
1. ?  1. Given 
2.

2. ? 
3.

3. The measure of an exterior

4. ?  4. Substitution 
5. ?  5. ? 
To prove:
The side
Given:
Consider the figure,
Figure
From figure
Equilateral
If the measure of one angle of a triangle is greater than the measure of a second angle, than the side opposite to the larger angle is longer than the side opposite to the smaller angle.
The measure of an exterior angle of a triangle is greater than the measure of either nonadjacent interior angle of a triangle.
Definition:
The triangle whose all the sides are equal and the measures of all the angle are same, that triangle is called equilateral or equiangular triangle.
Approach:
Consider an equilateral
Since, in equilateral triangle the measures of all the angle are same, then
Consider the triangle
Since, the measure of an exterior angle of a triangle is greater than the measure of either nonadjacent interior angle of a triangle. Then,
Substitute equation
Consider the triangle
Since, the measure of one angle of a triangle is greater than the measure of a second angle, than the side opposite to the larger angle is longer than the side opposite to the smaller angle. Then, from equation
PROOF  
Statements  Reasons 
1. Equilateral 
1 
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