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# Common Core Geoemtry. Chapter 2. Proof

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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 2 of my Common Core-aligned course in geometry. The topic is proof. Students are introduced to the concept of proof and then, at the end of the chapter, prove the fundamental angle relationships. Below is a description of the chapter's 9 sections.

2.1 Conjecture and Counterexample. Students are presented with a great variety of carefully chosen diagrams and are asked to make conjectures based on them.

2.2 Conditional Statements. A study of the structure and truth-conditions of conditional statements, with an emphasis on their relation to proof.

2.3 Related Conditionals. The three related conditional are defined, their truth-conditions are studied. Emphasis is placed on the equivalent of original and contrapositive and on the non-equivalence of original and converse.

2.4 Biconditionals. A discussion of the 'only if' construction is followed by a definition of 'iff'.

2.5 Proof Structure. The concepts of Given, Conclusion and Proof are defined. A proof is defined as a sequence of statements that begins with the Given and ends with the Conclusion such that the truth of each new statement is guaranteed by the truth of what's gone before. Students are asked to set up (but not complete) a number of proofs.

2.6 Indirect Proof. Some of the first proofs of the course are indirect. Thus a study of indirect proof must come early on. An Indirect Proof is analyzed in four parts: Given, Conclusion, Assumption and Reduction.

2.7 The Proofs of the Fundamental Angle Relationships. The first proof set of the year. Results proven include: right angles measure 90°, linear pairs are supplementary, perpendicular lines form four right angles, and vertical angles are congruent.

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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