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# Common Core Geometry. Chapter 7. Similarity

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So, this is the year when you have to switch over to the new Common Core Standards for high school geometry, but you don't quite know what that means. Or perhaps you know the new standards but haven't had time to re-align your course. I have your answer. I've created a set of PowerPoints and Word worksheets, aligned to the Common Core, that will take you from the first day of the course to the last.

This is Chapter 7 of my Common Core-aligned course in geometry. The topic is similarity. Below is a description of the chapter's six sections.

7.1 Ratios and Proportions, Parts 1 and 2. In Part 1, the algebraic solutions of proportions are reviewed. In part 2, examples of the use of proportions in concrete problem solutions are given. Students also learn how to prove proportions equivalent.

7.2 Scale Transformations, Parts 1 and 2. In Part 1, students are instructed in how to produce a scale transformation and are asked to make a number of conjectures about the scale images of segments and angles. In Part 2, students are introduced to the Scale Transformation Postulate. It states that the scale of a line segment is a second, parallel line segment whose length is given by kn, where k is the scale factor and n is the length of the preimage.

7.3 Similar Polygons. Similarity is defined as congruence after a scale transformation. It is proven that similar polygons have congruent angles and proportional sides. (Note that this is not a postulate, as it was before Common Core. It is proven on the basis of the Scale Transformation Postulate.)

7,4 The Similarity Tests, Parts 1 and 2. In Part 1, Angle-Angle Similarity is proven. In Part 2, SAS and SSS similarity are proven.

7.5 Parallel Lines and Proportional Parts. Key corollaries of the Similarity Tests are proven. These include the Triangle Proportionality Theorem, its Converse the Triangle Midsegment Theorem

7.6 Similarity Applications, Parts 1 and 2. Part 1 is a set of problems. Part 2 is a set of proofs. Each calls upon students to make use of the three triangle similarity tests - AA, SAS and SSS.

For each section, there is both a PowerPoint and a Word worksheet. The worksheets give ample practice in the day's topic. Also included are a Chapter Review and a Chapter Review Key.

The worksheets are appropriate for both Honors and non-Honors classes. Questions marked H are intended for Honors only. The chapter includes a Challenge problem set. It is intended for Honors students. Worksheets include answers to selected questions.

A description of the course can be found among my downloads. The title is "Course Contents with Commentary".
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2 Weeks
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