NOTES 3 8 7 2 Triangle Congruence HL
- Slides: 9
NOTES 3. 8 & 7. 2 Triangle Congruence HL and AAS
SSS (Side-Side) Postulate If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent. A B Y C ABC ≅ X Z XYZ
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. A Y B C ABC ≅ Z XYZ X
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-Side) Theorem • If two angles and a non-included side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the triangles are congruent.
IMPOSSIBLE METHODS: Angle-Side or Angle-Angle ASS or SSA – can’t spell bad word AAA – proves similar , not congruent . A Y B C ABC ≅ Z XYZ X
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 3 rd angles must be congruent. • AKA – No Choice Theorem • Triangles do not have to be congruent for this theorem.
