In this lesson, students use 1-inch strips with evenly spaced holes and metal paper fasteners to make conjectures about diagonals of quadrilaterals. Then they have a chance to practice using diagrams to recognize when the Side-Side-Side, Angle-Side-Angle, and Side-Angle-Side Triangle Congruence Theorems apply. There is an optional activity in this lesson where students apply triangle congruence theorems to a woodworking context.

Students have the opportunity to move through several stages of the proof process in this lesson as they develop conjectures, match diagrams to conjectures, consider which theorems apply, and write a summary of a proof.

As students analyze diagrams to see which triangle congruence theorems apply, they look for and make use of structure (MP7). The work of moving from conjectures to proof is another opportunity to look for and make use of structure and to construct viable arguments (MP3).