Download File - Miss Pereira

Geometry
Name: ______________________
(4-4 & 4-5) Triangles
Congruence Theorems
Date: ______________________
Objective: You will be able to determine if two triangles are congruent using the
triangle congruency theorems.
Triangle Congruency Theorems
Side-Side-Side Congruence Postulate (SSS): If the sides of one triangle are
congruent to the sides of a second triangle, then the triangles are congruent.
Side-Angle-Side Congruence Postulate (SAS): If two sides and the included angle of
one triangle are congruent to two sides and the included angle of a second triangle,
then the triangles are congruent.
Angle-Side-Angle Congruence Postulate (ASA): 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.
Angle-Angle-Side Congruence Postulate (AAS): If two angles and a non-included side
of one triangle are congruent to two angles and the non-included side of a second
triangle, then the triangles are congruent.
Hypotenuse-Leg (HL): RIGHT TRIANGLES ONLY!!
If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse
and one leg of a second right triangle, then the right triangles are congruent.
Example #1:
Are the following triangles congruent? If so, write a congruency
statement and state by which triangle congruency theorem.
1.
2.
3.
4.
5.
Example #2:
What other information do you need in order to prove these triangles congruent?
Example #3:
Name the two congruent triangles in this picture.