Angle-Angle Similarity Postulate

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Objective

SWBAT prove triangles are similar using the Angle-Angle Postulate.

Big Idea

Students use a variety of tools such as patty paper, rulers, and protractors to prove triangles are similar by comparing angle measurements.

Do Now

5 minutes

For today's Do Now, students are shown two triangles. They are told the triangles are similar and asked to explain what that means. Then they are instructed to write proportions for the sides. This is a review of the previous lesson. As students are working, I circulate to check that they understand the criteria for similarity. After about three minutes, we will go over the students' responses in a whole class discussion.

Mini-Lesson

10 minutes

At the beginning of today's Mini-Lesson, I will explain the Angle-Angle Similarity Postulate. As a class, we will discuss why it is only necessary to show that two pairs of angles in a triangle need to be congruent in order for the triangles to be similar. 

Next, I will show students a video demonstrating the task students will use to prove triangles are similar using the Angle-Angle Similarity Postulate. Then, we will practice drawing a pair of similar triangles and proving they are congruent. Before students begin the activity, I have them write down the Angle-Angle Similarity Postulate in their notebooks.

Activity

23 minutes

For today's Activity, my students are asked to draw three pairs of similar triangles and prove they are similar (G.SRT.3,  MP3). They can use a ruler and patty paper or a protractor to draw the triangles (MP5). Students are instructed to show all measurements, calculations, and write proportions and similarity statements. 

Using the method shown in the Mini-Lesson, students can replicate angles of a triangle. They sometimes have difficulty measuring angles and sides precisely. Inaccurate measurements affect the calculations of the proportions. If I see that students triangles appear similar, but the calculations don't work out as expected, I instruct students to go back to their figures and remeasure the sides (MP6).

Summary

5 minutes

At the end of today's lesson, I call on students to show their examples using the document camera and explain how they know their triangles are similar. We also discuss the reasons why proportions may not be exactly the same. 

In later lessons, students will use the Angle-Angle Similarity postulate to solve problems involving triangle similarity.