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In this section, students review the concept of a dilation and expand upon their understanding to notice properties such as angles remaining congruent after dilation and lines being taken to the same or parallel lines after dilation. Students practice writing equivalent ratios of segment lengths before and after dilation to find unknown lengths after the same dilation. Then, they examine...
In this section, students use the definition of similar figures to develop other conditions for guaranteeing similarity, especially in triangles. Students continue to develop their skills in making and proving conjectures by generalizing from a few examples.
Students develop the Angle-Angle Triangle Similarity Theorem, and an optional lesson allows students to explore other possible conditions for triangle similarity theorems.
In this section, students explore similar right triangles which allow for the use of the Pythagorean Theorem in addition to the properties of similar triangles. They also use the properties of similar triangles to prove the Pythagorean Theorem, then practice using proportional relationships and the Pythagorean Theorem together to find unknown lengths.