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# Overlapping Triangles

Lesson 9 of 10

## Objective: SWBAT persevere in proving triangles congruent when given overlapping triangles.

#### Do Now

*10 min*

This Do Now is a review of topics learned earlier in the unit and requires students to use vertical angles, isosceles triangle properties and sum of angles in a triangle. This is a great question to ask students to lead the discussion/review on - then the entire class can determine if they agree with each students' explanation or if they utilized a different strategy to find x (MP 3).

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#### Challenge Practice/Homework

*40 min*

After reviewing with students how to identify which pair of congruent triangles that we are trying to prove are congruent, we can let students work on these practice Challenge problems. The goal of these proofs is to ask students to persevere in proving more complicated triangle congruence proofs (MP 1). You can scaffold this lesson by asking students to focus on just one or two proofs and then reviewing these with the whole class.

This lesson works best when students present and explain the proof process (MP 3). Students also have the choice to write these proofs as flow proofs, if prefered.

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#### Exit Ticket

*10 min*

This formative Exit Ticket helps you to determine if students are able to recognize congruent triangles in overlapping triangle diagrams. This would be a good Exit Ticket to print and collect so that you can see if students are using visualize strategies (i.e. colors and shading) to identify triangles that are congruent.

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#### Triangle Proof Project

*20 min*

Depending on how you structure this lesson, you may want to begin some of the student presentations for the Triangle Video Proof Project. If time does not allow, then all students should be prepared to present the next day!

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- UNIT 1: Introduction to Geometry: Points, Lines, Planes, and Angles
- UNIT 2: Line-sanity!
- UNIT 3: Transformers and Transformations
- UNIT 4: Tremendous Triangles
- UNIT 5: Three Triangle Topics
- UNIT 6: Pretty Polygons
- UNIT 7: MidTerm Materials
- UNIT 8: Circles
- UNIT 9: 3-D Shapes and Volume
- UNIT 10: Sweet Similar Shapes
- UNIT 11: Trig Trickery
- UNIT 12: Finally Finals

- LESSON 1: Time for Triangles
- LESSON 2: Time for More Triangles
- LESSON 3: SSS for Real
- LESSON 4: SAS-sy Triangles
- LESSON 5: AAS and ASA Fun
- LESSON 6: HL and More Practice with Proofs
- LESSON 7: Isosceles Triangles Forever
- LESSON 8: On the Plane - Coordinate Geometry Proofs
- LESSON 9: Overlapping Triangles
- LESSON 10: Tremendous Triangles Projects