If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of a second triangle, then the triangles are congruent (AAS)

Given

Triangles ABC, EFG

AC = EG

Prove
 


Proof
1:
- Given
2: - From 1  - If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent

3: AC = EG - Given

4: - From 1,2,3 - If two angles  and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent (ASA).

Corresponding altitudes of congruent triangles are congruent

Given:


Altitudes CD to AB and TV to RS

 

Prove
CD = TV

Proof

1: AC = RT - correosponding sides in congruent triangles ( ) are equal

2: - correosponding angles in congruent triangles () are equal

3:  - Given (Altitudes CD to AB and TV to RS)

4:  - From 1,2,3 AAS - If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of a second triangle, then the triangles are congruent (AAS)

5: CD = TV - CPCTC - Congruent Parts  Congruent Triangles Congruent