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# Common Core Geometry. Chapter 9. Circles

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### PRODUCT DESCRIPTION

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 9 of my Common Core-aligned course in geometry. The topic is circles. Below is a description of the chapter's eight sections.

9.1 The Anatomy of a Circle. All relevant terms - circle, radius, diameter, arc, chord, central angle, etc. - are defined and illustrated.

9.2 Pi. The Common Core Standards stipulate the limit-type proofs should be employed where appropriate. Here a limit-type proof is given of the constancy of pi. Key is the idea of an inscribed regular polygon.

9.3 Arcs and Central Angles. It is postulated that arcs have the same measure and the central angles that cut them. A number of consequences are drawn, among them the Arc Addition Theorem.

9.4 The Arc/Chord Proofs. A number of fundamental results about arcs and their relations to chords are proven. Among them: equal chords cut equal arcs, a radius perpendicular to a chord bisects it, and the perpendicular bisector of a chord passes through the circle's center.

9.5 The Inscribed Angle Theorem. The Inscribed Angle Theorem is proven and applied. Emphasis is placed on inscribed polygons.

9.6 The Tangent Line. The concept of a tangent line is defined. It is proven that a line tangent to a circle is perpendicular to the radius drawn to the point of tangency. Applications of this and related theorems are given.

9.7 The Secant- Tangent Angle Theorems. A set of results to do with angles formed by secants and tangents is proven. Key here is the Inscribed Angle Theorem.

9.8 The Special Segment Theorems. A set of results to do with lengths of secants and tangents is proven. The set culminates with a proof of the Pythagorean Theorem, the second for the course.

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.

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

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