Unit 2: Congruence

Students prove that figures are congruent by reasoning about rigid transformations. They prove the Triangle Congruence Theorems (SSS, SAS, ASA), the Perpendicular Bisector Theorem, and several theorems about quadrilaterals.

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Concept

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Set 1

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What this unit covers

A Congruent Figures · 5 lessons

Goals

• Comprehend and generate congruence statements that establish corresponding parts.
• Justify whether or not figures are congruent by reasoning about rigid transformations.

Lessons

1. Congruent Parts, Part 1
2. Congruent Parts, Part 2
3. Congruent Triangles, Part 1
4. Congruent Triangles, Part 2
5. Points, Segments, and Zigzags

B Triangle Congruence Theorems · 6 lessons

Goals

• Identify situations where Side-Side-Side, Angle-Side-Angle, and Side-Angle-Side Triangle Congruence Theorems apply.
• Use previously proven theorems about triangles to write new proofs.

Lessons

1. Side-Angle-Side Triangle Congruence
2. Angle-Side-Angle Triangle Congruence
3. The Perpendicular Bisector Theorem
4. Side-Side-Side Triangle Congruence
5. Practicing Proofs
6. Side-Side-Angle (Sometimes) Congruence (Optional)

C Proofs about Quadrilaterals · 3 lessons

Goals

• Critique others’ justifications about quadrilaterals and constructions.
• Use previously proven theorems to write new proofs about quadrilaterals.

Lessons

1. Proofs about Quadrilaterals
2. Proofs about Parallelograms
3. Bisect It

D Let’s Put It to Work · 1 lesson

Lessons

1. Congruence for Quadrilaterals