Congruence Proofs
Congruent triangles are identical in shape and size. Using the four congruence conditions (SSS, SAS, AAS, RHS) we can prove triangles are congruent and deduce unknown measurements.
What You Need to Know
Key Concept Diagram
SSS: Three pairs of equal sides prove congruence
SAS: Two pairs of equal sides and the included angle prove congruence
AAS: Two pairs of equal angles and any corresponding side prove congruence
RHS: Right angle, hypotenuse, and one other side prove congruence in right triangles
Key Vocabulary
Congruent
Identical in shape and size; congruent figures can be mapped onto each other
SSS
Side-Side-Side: a congruence condition requiring three equal sides
SAS
Side-Angle-Side: two equal sides with the angle between them
Included angle
The angle between two specified sides of a triangle
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Two triangles have all three pairs of sides equal. Which congruence condition applies?
Question 2
Triangle ABC and XYZ have AB = XY, BC = YZ, and angle B = angle Y. Which condition proves congruence?
Question 3
When can you use the RHS congruence condition?
Key Concepts Summary
- ●SSS: Three pairs of equal sides prove congruence
- ●SAS: Two pairs of equal sides and the included angle prove congruence
- ●AAS: Two pairs of equal angles and any corresponding side prove congruence
- ●RHS: Right angle, hypotenuse, and one other side prove congruence in right triangles