Triangle Congruence HL and AAS NOTES 3.8 & 7.2 Triangle Congruence HL and AAS

SSS (Side-Side-Side) Postulate If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent. ABC ≅ XYZ A Y X Z B C

SAS (Side-Angle-Side) Postulate If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent. ABC ≅ XYZ A Y X Z B C

ASA (Angle-Side-Angle) Postulate 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.

AAS (Angle-Angle-Side) Theorem If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the triangles are congruent.

IMPOSSIBLE METHODS: Angle-Side-Side or Angle-Angle-Angle ASS or SSA – can’t spell bad word AAA – proves similar , not congruent . ABC ≅ XYZ A Y X Z B C

HL (Hypotenuse - Leg) Theorem: If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent. Example: because of HL. A X B C Y Z

Triangles are congruent by… SSS AAS SAS ASA HL

Theorem 53 If 2 angles of one triangle are congruent to 2 angles of another triangle, then the 3rd angles must be congruent. AKA – No Choice Theorem Triangles do not have to be congruent for this theorem.