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are similar, that in similar Rgures, corresponding angles are congruent and corresponding sides are in a proportional relationship, and the shortcut speciRc to similarity: Angle-Angle Triangle Similarity.
Students explicitly build on their work with congruence and rigid motions, establishing that triangles are similar by dilating them strategically and showing that after dilation, the congruence criteria they already established are met, and therefore a sequence of rigid transformations takes one triangle onto the dilation of the other, and the original triangles are related by a sequence of rigid motions and a dilation. By the deRnition of similarity in terms of transformations, the triangles are similar.
The unit balances a focus on proof with a focus on using similar triangles to Rnd unknown side lengths and angle measurements. Earlier in the unit, students prove theorems using rigid transformations and dilations. Later in the unit, students use similarity shortcuts, especially Angle-Angle Triangle Similarity, to justify that triangles must be similar and to Rnd unknown side lengths using the fact that side lengths in similar Rgures are in the same proportion.
This unit previews many of the important concepts that students rely on to make sense of trigonometry in later units. The latter part of the unit focuses on similar right triangles, and students preview trigonometric concepts by using the same right triangle to Rnd missing lengths and angle measures in several similar right triangles. In addition, students are introduced to some of the applications of right triangles that they will explore in more depth in the trigonometry unit, such as Rnding the heights of objects through indirect measurement.
Note on materials: For most activities in this unit, students have access to a geometry toolkit that includes tools that students can choose from strategically: compass and straightedge, tracing paper, colored pencils, and scissors. In some lessons, students will also need access to a ruler and protractor. In the Rnal section, Putting It All Together, there are optional activities involving going outside to measure the heights of tall objects. Students will need measuring tools and may also choose to use speciality materials such as small mirrors. Finally, there are some activities that are best done using dynamic geometry software, and these lessons encourage teachers to prepare to give students access to the digital version of the student materials.
G4 Right Triangle Trigonometry
Prior to beginning this unit students will have considerable familiarity with right triangles. They learned to identify right triangles as early as grade 4. Students studied the Pythagorean Theorem in grade 8, and used similar right triangles to build the idea of
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Course Guide