Properties of Isosceles Triangles

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Objective

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

Big Idea

Students will create a graphic organizer with the properties of isosceles triangles in order to write proofs.

Do Now

3 minutes

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.

 

Mini-Lesson

18 minutes

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. 

 

Activity

19 minutes

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.

 

Summary

5 minutes

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.