Integrated Math 1 / Unit 8: Transformations and Congruence
8.6 Triangle Congruence Criteria
Notes
You can show two triangles are congruent without checking all six parts.
- SSS: three pairs of equal sides. SAS: two sides and the included angle. ASA: two angles and the included side. AAS: two angles and a non-included side. HL: right triangles with equal hypotenuses and one pair of equal legs.
- AAA does not work (same shape, maybe different size). SSA does not work in general.
- Example: two triangles with angles $40^\circ$ and $60^\circ$ and an included side of 8 cm are congruent by ASA.
- Mark the given information first, then match to a rule.
Practice
Two triangles have two pairs of equal sides and the angle between those sides equal. Which criterion proves them congruent?
The angle is included between the two sides, which is SAS.
Which does NOT guarantee that two triangles are congruent?
Triangles with equal angles can be different sizes.
Two triangles each have angles of $40^\circ$ and $60^\circ$, and the side between those angles is 8 cm in both. Which criterion applies?
Two angles and the included side are equal, which is ASA.
Ready for more? Take the Unit 8 test.