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