Additional Properties of Triangles

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Objective

SWBAT prove theorems involving the properties of triangles using Geometer’s Sketchpad

Big Idea

Students will use Geometer's Sketchpad to investigate properties of a triangle's mid-segment and median. They will also investigate properties of isosceles triangles.

Do Now

7 minutes

In today's Do Now, students define the terms midpoint of a segment and perpendicular bisector of a segment. After they define the terms they construct a segment and its perpendicular bisector using a compass and a straightedge.

During this lesson we will use Geometer's Sketchpad to explore this construction. While my students are working on the Do Now, I hand out the laptops, ask students to sign on, and to open Geometer's Sketchpad.

Mini-Lesson

5 minutes

When we use Geometer's Sketchpad, I often let the students play a little bit. In today's Mini-Lesson, we begin with about 3 minutes of unstructured time to explore the program. Since my students have used this program in earlier lessons, they know how to do a few things. Usually, it takes some students a few minutes to get their Sketchpad-on. I find things work better when I give students this time to explore (or to practice) before starting the activity. 

As they explore, I start to make some suggestions. I display a practice sketch and I encourage students to see if they can construct the midpoint of a segment and using the midpoint to construct a perpendicular bisector for the segment. I also remind students that they should know how to measure segments and angles. All of these skills will be useful during today's Sketchpad activity. 

Activity

28 minutes

I like my students to work in pairs on Sketchpad activities, but I ask each student to complete end submit an Activity Sheet

For each part of Additional Properties of Triangles Activity, students are required to create a new page in their Sketchpad document. On each page students work together to create a dynamic construction modeling a theorem or a property of triangles (MP4, MP5). As they explore the construction, I encourage them to discuss the theorems with their partners. For each construction, each student should write answers to questions and explain why their answers are correct (MP3).  

As my students are working, I circulate around the room and help students who need assistance or who have a question. Some will need help finding the commands on the program. When possible, I like to have other students help each other with using Sketchpad.

Throughout the activity, I have mini discussions with students. I ask students to stop for a second and we go over certain questions. This helps me see how my students are doing, and to give them guidance with their investigation. Today, I plan to focus on Part A Question 2 and Part B Question 2 as checkpoints. 

At the end of the today's activity, I will collect the activity sheet. I will not check the .gsp files, but I have asked the students to make sketches on their worksheets. 

Summary

5 minutes

At the end of the lesson, I have my students add the theorems that we have covered over the last few days to their theorem list in their notebook. 

These theorems are:

  • The mid-segments of triangles are half the length of and parallel to the third side of the triangle. 
  • The medians of a triangle intersect in a point. 
  • The median of the vertex of an isosceles triangle is the perpendicular bisector of the base and the angle bisector of the vertex. 
  • The base angles in an isosceles triangle are congruent.

Students will use these theorems in later lessons to write proofs.