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

2. 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

3. 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

4. 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.

5. 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.

6. 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

7. 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

8. Triangles are congruent by…
SSS AAS
SAS ASA HL

9. 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.