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# Common Core Geometry. Chapter 5. Inequality

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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 5 of my Common Core-aligned course in geometry. The topic is inequality. Students prove the triangle inequalities and apply those results. They also prove that the shortest path from a point to a line and between parallel lines is the length of the perpendicular which connects them. Below are descriptions of the chapters six sections.

5.1 Inequalities in One Triangle. The section begins with a review of the Triangle Exterior Angle Inequality. It is the fundamental inequality, the one used to prove all the rest. Students then prove both the Triangle Angle-Side Inequality (the greater side lies opposite the greater angle) and the Triangle Side-Angle Inequality (the greater angle lies opposite the greater side).

5.2 Applications. Students apply the three inequalities proven in the previous section - the Triangle Exterior Angle Inequality, the Triangle Side-Angle Inequality and the Triangle Angle-Side Inequality.

5.3 The Triangle Inequality. Students are guided through a proof of the Triangle Inequality. The proof is followed by a set of applications. Given three positive quantities, students are asked to determine whether they could represent the side length of a triangle. Students are given two positive quantities and are asked to find the range of possible values for the third side.

5.4 Distance. It is proven that the distance from point to line is the length of the perpendicular from one to the other. It is also proven that the distance between a pair of parallel lines is the length of the perpendicular between them. The section ends with a discussion of altitudes in a triangle. Three possibilities are distinguished: an altitude internal to the triangle, an altitude coincident with a side, and an altitude external to the triangle.

5.5 The Hinge Theorem and its Converse. Students draw upon the inequalities of 5.1 to prove the Hinge Theorem (or SAS Triangle Inequality) and its Converse (or SSS Triangle Inequality).

5.6 Applications. The chapter ends with a set of problems in which the Hinge and Converse Hinge are applied.

For each section there is both a PowerPoint and a worksheet. The worksheets give ample practice in the day's topic. Answers are included.

The worksheets are appropriate for both Honors and non-Honors classes. Questions marked H are intended for Honors only. Worksheets include answers to selected questions.

Included is a challenge problem set, appropriate for an Honors-level class. It is intended to be given out on the first day of the chapter and taken up on the last day.

The Preview is is a selection of PowerPoints and worksheets from the chapter.

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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