4-4+ASA+and+AAS+Congruence+Thms

The purpose of this chapter is to prove that two triangles are congruent using ASA and AAS. (Textbook page 220)

ASA (Angle Side Angle) If two angles and the included side (side between the angles) of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

Example: Prove these triangles are congruent using ASA. Given, Ð ABD @Ð CBE, AD is an included side, CE is an included side. AD @ CE. DE is parallel to AB.

AAS (Angle Angle Side) If two angles and a non-included side (outside the two angles) of one triangle are congruent to two angles and a non-included side of another triangle, then the two triangles are congruent. Example: Describe how to prove a triangle could be congruent to another by using AAS If two triangles have two congruent angles and a congruent non-included side than the triangles are congruent

Problems for you Which one of these triangles is not congruent to the one next to it?



Which theorem can be used to prove these 2 triangles congruent?



Are these triangles congruent? Yes. BUT WHY?!!



AB is parallel to CD, and point E bisects BC. Use ASA or AAS to prove the triangles congruent.

Links [] http://www.jimloy.com/geometry/congruen.html