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# Properties of Isosceles Triangles

Lesson 10 of 11

## Objective: SWBAT write two-column proofs involving the properties of isosceles triangles.

#### Do Now

*3 min*

For today, rather than writing notes directly in their notebooks, I plan to have students use a graphic organizer. The notes for today's lesson will focus on the **properties of an isosceles triangle**.

To get things rolling, today's Do Now asks students to fold three pieces of different colored paper creating a graphic organizer with 6 tabs. The task is based on one of Dinah Zike’s foldables. I expect that the different colors of the papers and the manipulative aspect of the organizer will help my students to better remember the concepts written on their graphic organizer.

#### Resources

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#### Mini-Lesson

*18 min*

The goal of today's mini-lesson is for students to fill in the 6-tab graphic organizer they created during the Do Now. I will project the Properties of Isosceles Triangles Presentation on the Smart Board. Inside each tab, students write theorems and/or definitions pertaining to the statement on the tab as shown in the presentation (MP6). As we discuss the slides I plan to ask my students to draw a diagram, write down given statements, and a prove a statement. Students will use their graphic organizer to support their planning for a two-column proof.

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#### Activity

*19 min*

Using their graphic organizers, students will now write three proofs. They will actually record the proofs on the last tab of their organizers. The proofs ask students to prove that in an isosceles triangle, the triangles on each side of the altitude are congruent. Students are expected to prove this conjecture in three different ways, using the SAS, SSS, and ASA postulates to write formal two-column proofs.

My plan is to group my students into heterogeneous trios and assign each student in the group a different proof. After about 5 minutes, the students will take turns sharing their proofs within their groups. Afterward, each student in responsible for writing down all three proofs.

At the end of the activity section, we go over the three proofs. I call on one of the students from a group and ask him or her to explain the proof. It doesn't have to be the proof he or she had originally written since the groups member each explained the proof to the rest of the group.

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#### Summary

*5 min*

As a summary reflection about today's lesson, I ask students to write in their notebook about which proof they felt was the easiest to write. After about two minutes of writing, we discuss their answers as a whole class.

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- UNIT 1: Preparing for the Geometry Course
- UNIT 2: Geometric Constructions
- UNIT 3: Transformational Geometry
- UNIT 4: Rigid Motions
- UNIT 5: Fall Interim Assessment: Geometry Intro, Constructions and Rigid Motion
- UNIT 6: Introduction to Geometric Proofs
- UNIT 7: Proofs about Triangles
- UNIT 8: Common Core Geometry Midcourse Assessment
- UNIT 9: Proofs about Parallelograms
- UNIT 10: Similarity in Triangles
- UNIT 11: Geometric Trigonometry
- UNIT 12: The Third Dimension
- UNIT 13: Geometric Modeling
- UNIT 14: Final Assessment

- LESSON 1: Triangle Inequality Theorem Investigation
- LESSON 2: Side-Side-Side
- LESSON 3: Angles of Triangles
- LESSON 4: Relationships between Angles and Sides of a Triangle
- LESSON 5: Applying Triangle Angle Theorems
- LESSON 6: Side-Angle-Side
- LESSON 7: Angle-Side-Angle
- LESSON 8: CPCTC
- LESSON 9: Additional Properties of Triangles
- LESSON 10: Properties of Isosceles Triangles
- LESSON 11: Properties of Isosceles Triangles Alternative Lesson with Dynamic Geometry Software