Similar Triangles using Geometer's Sketchpad

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Objective

SWBAT investigate properties of similar triangles using dynamic geometry software.

Big Idea

Students use Geometer's Sketchpad to investigate properties of similar triangles, which share a vertex and have parallel bases.

Do Now

7 minutes

As my students enter the classroom, I assign them a partner and give each pair a laptop. For today's Do Now, I ask my students to practice using Geometer's Sketchpad. They know a number of different skills at this point. I'd like them to maintain these skills, so a little practice is always worthwhile. 

Today, my students will work in pairs to complete the main activity using Geometer's Sketchpad. Although I have enough computers for the students to work independently, I find that by pairing them they are able to participate in mathematical discourse and can help each other use the computer program. 

Mini-Lesson

3 minutes

Students have used Geometer's Sketchpad several times throughout the year. Each time they use it, they become more familiar with how it works and what it can do. For the Mini-Lesson, we go over the Do Now. I ask students to state the commands that answer the questions. 

Activity

30 minutes

I have prepared a worksheet with specific instructions for my students to follow. There are also a series of guiding questions. The questions should lead the students to discover (or review) several properties of similar triangles. The activity introduces students to triangle similarity and allows them to come up with their own conclusions (G.SRT.4, G.SRT.5, MP3). 

As they work, I circulate and check their sketches. I see if the sketches pass the drag test. I drag the vertices and lines of the diagrams to see if they maintain the properties. For this activity, my students often draw lines that look parallel instead of constructing lines that are parallel. The more often we use Geometer’s Sketchpad, the better students get at using the program.

After about 20 minutes, I will have the students shut down their computers and work offline on Questions 5 and 6 from the worksheet. For these two problems, students must apply concepts learned in the investigation to find the measure of missing sides in similar triangles. At the end of the activity, I call on two students to show their answers and explain their work.

Summary

5 minutes

At the end of the lesson, I will lead a discussion to review the activity. I will ask students to explain their findings. When we go over Question_1, I expect my students to recognize that the angles are congruent because they are corresponding angles formed by two parallel lines intersected by a transversal. Using this information, I hope that they found that the sides of the Triangles were in the same proportion. I explain that this is an important criteria for similarity. After we discuss the activity, I will ask my student to take a few minutes and write a summary in their notebooks.

The concepts learned today using Sketchpad will be explored during the next few lessons.