1. Investigating Triangles
Congruent triangles: two triangles are congruent if their corresponding parts are congruent.
SSS (Part 1 Triangle) Side-Side-Side Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.

2. SAS (Part 2 Triangle) Side-Angle-Side Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and an included angle of another triangle, then the triangles are congruent.
ASA, (Part 3 Triangle) Angle-Side-Angle Congruence Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

3. AAS (Part 4 Triangle) Angle-Angle-Side Congruence Postulate If two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, the two triangles are congruent.

4. AAA (Part 5 Triangle)
Angle-Angle-Angle Many different triangles can be constructed when given three angles.
ASS or SSA (Demonstrated with straws and pin.)
More than one triangle can have two sides and one angle in common if the angle is not included between the sides (SAS).

5. Application: Is it always necessary to show that all of the corresponding parts of two triangles are congruent to be sure that the two triangles are congruent?
For example, if you are designing supports for the beams in a roof, must you measure all three sides and all three angles to ensure that the supports are identical?
Or is checking 3 measurements enough to ensure that all braces will be identical? You can use congruent triangles to solve many real-life problems such as those found in designing and constructing buildings and bridges.

6. Homework:
Draw pairs of congruent triangles to represent the four congruence postulates. Label each heading (SSS, ASA, SAS, AAS) and use appropriate tick marks to identify congruent parts.