Triangle Similarity Review

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SWBAT prove that triangles are similar and use properties of similar triangles to solve special right triangles. Students will understand properties of special right triangles and other similar polygons.

Big Idea

Students work in cooperative learning teams as they practice concepts and skills related to triangle similarity.

Lesson Opener

10 minutes

Present the warm-up problem (5 minutes).  The warm-up problem for this lesson (found in the slide show) asks students to show that two angles are congruent using an angle relationship.  This could be part of a proof that two triangles are similar.

This lesson opener follows our Team Warm-up routine. 

Motivate the lesson (3 minutes).  I planned this lesson to address mistakes that many students made on the previous quiz.  I told students that this lesson was their chance to ask questions and practice before the unit test.


Review learning targets and the agenda for the lesson (2 minutes).   Display the agenda and learning goals for the lesson as you distribute materials for the activity.  Ask students to read them over and invite questions. 


40 minutes

Before class, print the Triangle Similarity Review Practice Activity handout. Make one copy for every two students and cut into half-sheets.  You may want to make a few extra copies, in order to allow students to start over with a fresh sheet if they go down the wrong path.  Distribute the half-sheets to the teams.   Tell the students that they are work in pairs to complete the problems. 

I used a Kagan Structure (Rally Coach).  My students learn the rules and roles for this mini-activity at the beginning of the school year, so it is a classroom routine.  The instructions are in the slide show.

As students are working, circulate around the classroom.  Common problems to look for:

  • Students may not use correct notation.    


Have students practice solving special right triangles (15 minutes).   The practice activity is intended to be completed using individual white boards.  The problem set (found in the slide show)  is displayed using the document projector.  Problems are presented in pairs, allowing students to work at different speeds.  Students may choose to complete either the problem on the left or the problem on the right.  Ask students to write the number of the problem they completed.   Insist that students show their work, both to help you make corrections when necessary and so that they can explain their thinking to teammates who may need their help.  Students hold their whiteboards in the air when they are finished with a problem so that you can check it.  If students are working fast, they should complete both problems in each pair, but all students should concentrate on answering one problem of each pair correctly first. 

As students are working, circulate around the classroom.  Common problems to look for:  

  • Students who are confused may erase their work before you have time to come around and check it.  Ask those students to concentrate on working a single problem to completion and not to be concerned with how fast others are working.  Stay with a student if necessary, to give them support and ensure that they have success.

Lesson Close

5 minutes

Have students reflect on the lesson in pairs and teams (5 minutes).  Students share in pairs, then in teams.  Teams report out by listing three important things they learned on the white board.

I used a Kagan Structure (Timed Pairs Share), with a few modifications.  The instructions are in the slide show.