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Students follow an interactive proof showing that vertical angles are congruent. The purpose of the exercise is to introduce vertical angles so that students can use this knowledge to understand angle pairs formed by parallel lines cut by a transversal and why some of these pairs are congruent. Students then follow a second proof showing that the sum of the interior angle measures of a triangle is 180°.
In the second module, students explore triangle similarity criteria, including Angle-Angle Similarity, or AA Similarity. Students solve a variety of problems involving triangle similarity using AA and the special angle pairs they learned about in the previous lesson. At the end of this lesson, students learn about the relationship between an exterior angle of a triangle and the two remote interior angles. Students solve simple problems using this knowledge as well.
Finally, students practice solving a variety of word problems, both challenging and more straightforward, using all the things they learned in the previous two lesson. Students are briefly introduced to the idea that the angles opposite the congruent sides in an isosceles triangle are congruent.
Module 1 Video
This video demonstrates that any translation of a line produces either an identical line or a parallel line and that rigid motions like translations preserve lengths and angle measures. This sets the stage for explaining why corresponding angles are congruent, and knowing about vertical angles helps to establish the congruences of the other angle pairs—alternate interior angles and alternate exterior angles.