Circles and the Pythagorean Theorem

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Presentation transcript:

Circles and the Pythagorean Theorem Lesson 9.6 Circles and the Pythagorean Theorem In Chapter 6, you discovered a number of properties that involved right angles in and around circles. In this lesson you will use the conjectures you made, along with the Pythagorean Theorem, to solve some challenging problems. Let’s review two conjectures that involve right angles and circles. Tangent Conjecture: A tangent to a circle is perpendicular to the radius drawn to the point of tangency. Angles Inscribed in a Semicircle Conjecture: Angles inscribed in a semicircle are right angles. Tangent Segments Conjecture: Tangent segments to a circle from a point outside the circle are congruent. The following are two examples that use circle conjectures and dissections, special right triangles, and the Pythagorean Theorem. JRLeon Geometry Chapter 9.6 HGSH

Circles and the Pythagorean Theorem Lesson 9.6 Circles and the Pythagorean Theorem JRLeon Geometry Chapter 9.6 HGSH

Circles and the Pythagorean Theorem Lesson 9.6 Circles and the Pythagorean Theorem JRLeon Geometry Chapter 9.6 HGSH

Circles and the Pythagorean Theorem Lesson 9.6 Circles and the Pythagorean Theorem JRLeon Geometry Chapter 9.1-9.2 HGSH

Circles and the Pythagorean Theorem Lesson 9.6 Circles and the Pythagorean Theorem JRLeon Geometry Chapter 9.1-9.2 HGSH

Circles and the Pythagorean Theorem Lesson 9.6 Circles and the Pythagorean Theorem JRLeon Geometry Chapter 9.1-9.2 HGSH

Circles and the Pythagorean Theorem Lesson 9.6 Circles and the Pythagorean Theorem JRLeon Geometry Chapter 9.1-9.2 HGSH

Circles and the Pythagorean Theorem Lesson 9.6 Circles and the Pythagorean Theorem JRLeon Geometry Chapter 9.1-9.2 HGSH

Circles and the Pythagorean Theorem Lesson 9.6 Circles and the Pythagorean Theorem Classwork: 9.6 Pages 509-510: problems 1 thru 16 JRLeon Geometry Chapter 9.1-9.2 HGSH