If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

Given

Triangles ABC, EFG


Prove


Proof
1:
- Given

2: - From 1

3:
- In a triangle, the sum of the measures of the interior angles is 180°

4: - From 3

5: - substitute 2 in 4

6: - From 5

The measure of an exterior angle of a triangle equals the sum of the measures of the two nonadjacent interior angles

Given

Triangle ABC

Exterior angle of a triangle

  - Two adjacent angles form a straight line (BC)

Prove

Proof

1:  - In a triangle, the sum of the measures of the interior angles is 180°

2: - If the exterior sides of two adjacent angles form a straight line, these angles are supplementary

 - From 1 and 2

In a triangle, the sum of the measures of the interior angles is 180°

Given:
 Triangle ABC

Prove:



Proof:

Through C, draw ED||AB

1: - The angles on segment ED

2:
- alternate interior angles are congruent, ED||AB, transversals: AC, BC


- From 1, 2