Throughout this unit, students have proved a variety of figures congruent. They started with segments (2 vertices), then triangles (3 vertices), and now are proceeding to the next most complicated geometric structure, quadrilaterals (4 vertices).
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. Finally, students match diagrams with statements about quadrilaterals, and write a proof using the analyses they did earlier.
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, as well as construct viable arguments (MP3).
- Generate (orally and in writing) conjectures about quadrilaterals.
- Identify situations where Side-Side-Side, Angle-Side-Angle, and Side-Angle-Side Triangle Congruence Theorems apply, and use them to prove theorems (in writing).
- Let’s practice what we’ve learned about proofs and congruence.
For the activities in this lesson and the next section, students will need strips cut from copies of the blackline masters. Prepare enough 1-inch strips with evenly-spaced holes so that every student gets 2 longer strips and 2 shorter strips. Put each set of strips in an envelope. Prepare one envelope for each student. To prepare the strips and fasteners to be used throughout the unit, include 4 metal fasteners in each envelope.
- I can use the Side-Side-Side, Angle-Side-Angle, and Side-Angle-Side Triangle Congruence Theorems in proofs.
- I can write conjectures about quadrilaterals.
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