This document discusses different methods for proving that triangles are congruent: SSS, SAS, ASA, AAS, and HL. It defines congruent polygons as having the same size and shape, meaning all corresponding sides are the same length and all corresponding angles have the same measure. The order of letters in a congruence statement indicates which angles or sides are being shown as congruent to prove the triangles are congruent.

1. PROVING TRIANGLES ARE
CONGRUENT

2. Proving Triangles are Congruent
 Definition of Congruent Polygons
 Congruence Statements
 SSS congruence
 SAS congruence
 ASA congruence
 AAS congruence
 HL congruence
 CPCTC

3. Definition of Congruent Polygons
 Polygons are congruent if
they are the same size and shape.
 Size: All corresponding sides are the same length
 Shape: All corresponding angles have the same measure.

4. Congruence Statements
 Congruence Statement:
 The order of the letters tells you which angles and
sides are congruent.

5. Side-Side-Side Congruence (SSS)
 Triangles are congruent if all 3 pairs of
corresponding sides are congruent.

6. Side-Angle-Side Congruence (SAS)
 Triangles are congruent if two pairs of
corresponding sides are congruent AND the pair of
included angles are congruent.

7. Angle-Side-Angle Congruence (ASA)
 Triangles are congruent if two pairs of
corresponding angles are congruent AND the pair
of included sides are congruent.

8. Angle-Angle-Side Congruence (AAS)
 Triangles are congruent if two pairs of
corresponding angles are congruent AND a pair of
non-included sides are congruent.

9. Hypotenuse-Leg Congruence (HL)
 Right Triangles are congruent if the corresponding
hypotenuses are congruent AND one pair of
corresponding legs are congruent.

10. CPCTC
 Corresponding Parts of Congruent Triangles are
Congruent.
SSS
SAS
ASA
AAS
HL