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# Common Core Geometry. Chapter 4. Parallels

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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 4 of my Common Core-aligned course in geometry. The topic is parallels. Below is a description of the chapter's seven sections.

4.1 Parallel Lines and Transversals. Here I provide the definitions of the new terms of the chapter - parallel, skew, transversal, alternate interior, alternate exterior, corresponding and consecutive interior.

4.2 The Triangle Exterior Angle Inequality. The Triangle Exterior Angle Inequality (TEAI) is the first of the chapters two postulates. It is the foundation of the Tests for Parallel found in 4.3.

4.3 Tests for Parallels. By use of the TEAI, we can easily prove that if two lines are cut by a transversal such that alternate interior angles are congruent, then those two lines are parallel. This is the first of the Tests. The others - the Alternate Exterior Angles Test, the Corresponding Angles Test and the Consecutive Interior Angles Test - follow from it immediately.

4.4 The Playfair Postulate and its Consequences. The Common Core Standards ask that we break from the current crop of texts. They give two parallel postulates. The CCS give only one, the Playfair Postulate. It says: through a point not on a line, there's at most one line parallel to the given line. By use of Playfair and the TEAI, it can be proven that when parallel lines are cut by a transversal, alternate interior angles are congruent. This is the first of the Parallel Consequences. The others follow from it immediately.

4.5 Parallel Application Proofs and Problems. Here students are given the opportunity to put the Parallel Tests and Parallel Consequences to work in a set of proofs and problems.

4.6 The Triangle Angle Sum Theorem and its Corollaries. First the Triangle Angle Sum Theorem is proven. After follows proofs of its important corollaries: a right (or obtuse) triangle has at most one right (or obtuse) angle, the non-right angles of a right triangle are acute and complementary, if two angles of one triangle equal two angles of another, then their third angles are equal too. Included is my Triangle Cut-and-Fold Project. It's a one-day project in which students are led to conjecture both the Triangle Exterior Angle Theorem (the measure of a triangle exterior angle equals the sum of the measures of its remotes) and the Triangle Angle Sum Theorem. The conjectures are followed by proofs.

4.7 AAS and HL Congruence and Converse ITT. The proof of the AAS triangle congruence principle is most easily given if the Triangle Angle Sum Theorem is already in place. AAS in turns makes a proof of HL congruence and Converse ITT a simple matter.

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

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.

The Preview is a selection of PowerPoints and Word worksheets.

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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