Students will investigate the essential question, “How can we use triangle congruence to prove when two shapes are exactly the same size and shape?” Teams will examine a real structure or design, create a geometric model, and use rigid motions and triangle congruence criteria to justify relationships within it. Through shared decision-making, critique, revision, and a brief presentation, students will communicate a logical proof and reflect on how their contributions strengthened the team’s solution.

Students will use rigid motions and corresponding sides and angles to determine whether two triangles are congruent. They will apply valid triangle congruence criteria to solve problems and prove relationships within geometric figures. Guided by the question, “How can we use triangle congruence to prove when two shapes are exactly the same size and shape?”, students will compare multiple proof strategies and justify their reasoning with precise diagrams and mathematical evidence. Teams will share decisions, resolve disagreements using evidence, present clear arguments, and reflect on their growth as mathematical problem-solvers.

Teams will create an annotated design of a local structure, public space, or pattern that contains pairs of triangles. They will produce a congruence evidence map identifying corresponding sides and angles, applying valid criteria, and modeling a rigid motion that maps one triangle onto another. The final product will be a visual proof board or digital presentation that answers, “How can we use triangle congruence to prove when two shapes are exactly the same size and shape?” Each student will also submit a brief reflection explaining one team decision, one problem-solving contribution, and how the evidence supports the proof.

Present teams with two triangular support-brace designs for a proposed community structure and ask whether the pieces are exactly the same size and shape without tracing or stacking them. Students measure selected sides and angles, test translations, rotations, or reflections with transparent overlays, and record evidence supporting or challenging congruence. Teams compare approaches, identify what information is sufficient, and revise their claims after a brief gallery walk. Close by asking, “How can we use triangle congruence to prove when two shapes are exactly the same size and shape?”

Host a “Congruence Proof Gallery” where teams display a real-world design containing two triangles they prove are congruent using rigid motions, corresponding parts, and a valid congruence criterion. Each team gives a two-minute presentation answering, “How can we use triangle congruence to prove when two shapes are exactly the same size and shape?” Visiting classmates, teachers, or community members leave feedback about the proof’s clarity and ask one mathematical question. Conclude with individual reflections on how collaboration, revision, and evidence strengthened each team’s solution.