Geometry · Quick Reference

Congruence Cheat Sheet

Geometry · Lesson 5/16

In one line: two figures are congruent if they are exactly the same shape and size — one could be placed perfectly on top of the other after moving, flipping, or rotating it.

Key Ideas

1Congruent Figures. Figures with identical shape and size; all corresponding sides and angles are equal.

2Congruence Notation. Written with a special symbol, but described in words as 'triangle ABC is congruent to triangle DEF', meaning every corresponding part matches.

3SSS (Side-Side-Side). If all three sides of one triangle equal all three sides of another, the triangles are congruent.

4SAS (Side-Angle-Side). If two sides and the angle between them match another triangle's two sides and included angle, the triangles are congruent.

5ASA (Angle-Side-Angle). If two angles and the side between them match another triangle's two angles and included side, the triangles are congruent.

Worked Examples

Triangle ABC has sides 5, 6, 7. Triangle DEF has sides 5, 6, 7. Are they congruent?

Yes, congruent by SSS

Two triangles share two equal sides and the included angle between them is also equal. What congruence rule applies?

SAS (Side-Angle-Side)

If triangle ABC is congruent to triangle DEF, and angle A = 50°, what is angle D?

Angle D = 50°

Practice Yourself

If two triangles have all 3 sides equal, what rule proves congruence?

SSS

If two triangles share 2 angles and the included side, what rule applies?

ASA

What does CPCTC stand for?

Corresponding Parts of Congruent Triangles are Congruent

Do congruent figures have to be the same size?

Yes