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 1inch strips with evenlyspaced 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 SideSideSide, AngleSideAngle, and SideAngleSide 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).
Lesson overview
 10.1 Warmup: Brace Yourself! (5 minutes)

10.2 Activity: Card Sort: More Practice Seeing Shortcuts (15 minutes)
 Includes "Are you Ready for More?" extension problem
 10.3 Activity: Matching Pictures to Proofs (10 minutes)
 Lesson Synthesis
 10.4 Cooldown: Practice Proving (10 minutes)
Learning goals:
 Generate (orally and in writing) conjectures about quadrilaterals.
 Identify situations where SideSideSide, AngleSideAngle, and SideAngleSide Triangle Congruence Theorems apply, and use them to prove theorems (in writing).
Learning goals (student facing):
 Let’s practice what we’ve learned about proofs and congruence.
Learning targets (student facing):
 I can use the SideSideSide, AngleSideAngle, and SideAngleSide Triangle Congruence Theorems in proofs.
 I can write conjectures about quadrilaterals.
Required materials:
 1inch strips cut from card stock with evenlyspaced holes (short strips/long strips)
 Geometry toolkits
 Metal paper fasteners
 Preprinted cards, cut from copies of the blackline master
Required preparation:
 For the activities in this lesson and the next section, students will need strips cut from copies of the blackline masters.
 Prepare enough 1inch strips with evenlyspaced 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.
Standards:
 This lesson builds on the standards: CCSS.7.G.A.2MS.7.G.2CCSS.HSGCO.B.8MS.GCO.8MO.7.GM.A.2aMO.G.CO.B.7
 This lesson builds towards the standards: CCSS.HSGCO.C.11MS.GCO.11MO.G.CO.C.10
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