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# Common Core Geometry. Chapter 1. The Language of Geometry

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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 1 of my Common Core-aligned course in geometry. The topic is the basic vocabulary of geometry. Below I describe the chapter's nine sections:

1.1 Definition, Postulate, Theorem. An introduction to the fundamental structure of geometry. Key here are the concepts of definition, postulate and theorem. Students are given examples of simple definition/postulate/theorem systems.

1.2 Points, Lines and Planes. An introduction to the fundamental objects of geometry - points, lines and planes. Emphasis is placed on precision of the relevant definitions.

1.3 The Point, Line and Plane Postulates. The postulates that govern the interaction of points, lines are stated and discussed. These include the Line Existence Postulate, the Plane Existence Postulate, the Plane/Plane Intersection Postulate and the Line/Plane Intersection Postulate.

1.4 The Algebraic Postulates. In section 1.5, we say that real numbers and points are the same mathematical objects from different points of view. Thus we should take a moment to remind students of the 'rules' that govern the reals. These are the Algebraic Postulates.

1.5 Segments and their Measures. A first statement of the Segment Addition and Ruler Postulates, the fundamental tools for distance measure.

1.6 Angles and their Measures. The section begins with the definition of angle and follows with a first statement of the Angle Addition and Protractor Postulates, the fundamental tools for angle measure.

1.7 Angle Relationships. The fundamental angle relationships are defined and illustrated. Included: adjacent, linear pair, vertical angle, supplementary and complementary.

1.8 Angle Categorization. With Euclid, we say that by definition equal linear pairs are right. By means of Angle Addition, all other angles are then categorized.

1.9 Polygons. Students are led to the correct definition of polygon, a nontrivial problem. Polygons are classified as regular and irregular, concave and convex.

For each section, there is a PowerPoint and a Word worksheet that gives students ample practice in the concepts covered.

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 exercise appropriate for Honors-level students. It is intended to be given out at the start of the chapter and then turned in at the end. Also included is a set of exercises labeled 'Topics'. These optional exercises give teachers the opportunity to extend the results of the chapter.

A description of the course can be found among my downloads. The title is "Course Contents with Commentary". The sample file is a selection of worksheets and PowerPoints from the chapter.
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2 Weeks
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