Triangle Congruence Theorems Geometry Notes – 4.2/4.3 Mr. Belanger

Importance Used to prove triangles congruent Gives many options for proving congruence Will continue to be used following this chapter

SSS Congruence Theorem Side – Side – Side Congruence: If three corresponding sides in two triangles are congruent, then the triangles are congruent.

SAS Congruence Theorem Side – Angle – Side Congruence: If, in two triangles, two sides and the included angle (formed by the two sides) are congruent, then the triangles are congruent.

ASA Congruence Theorem Angle – Side – Angle Congruence: If, in two triangles, two angles and the side connecting them are congruent, then the triangles are congruent.

AAS Congruence Theorem Angle – Angle – Side Congruence: If, in two triangles, two angles and the non-included (not between) side are congruent, then the triangles are congruent.

Try to decide if the triangles are congruent and if so, why? Examples: Try to decide if the triangles are congruent and if so, why? SAS

Try to decide if the triangles are congruent and if so, why? Examples: Try to decide if the triangles are congruent and if so, why? NO! AAA not a congruence theorem                                                                  

Examples: In triangle ADB and ADC, angle A is congruent to both, side AD is congruent to both and sides BD = CD.                                                         It’s obvious that ADB and ADC are not congruent. Be careful about just matching up any three parts like SSA. It has to be one of the four theorems.

Examples: Are the triangles congruent? Yes, AAS

Now memorize these four theorems!