MCC 9 12 G C 2 MCC 9

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(MCC 9‐ 12. G. C. 2; MCC 9‐ 12. G. C. 3)

(MCC 9‐ 12. G. C. 2; MCC 9‐ 12. G. C. 3)

© 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

© 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

1. Construct a large circle. 2. Construct a diameter. Label it AB. 3. Inscribe

1. Construct a large circle. 2. Construct a diameter. Label it AB. 3. Inscribe 2 angles in the same semicircle. Make sure the sides of each angle pass through A and B. 4. Measure each angle. What do you notice? A © 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia B

© 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

© 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

1. Construct a circle. 2. Select four points on the circle. 3. Construct a

1. Construct a circle. 2. Select four points on the circle. 3. Construct a quadrilateral by connecting those points. 4. Measure each of the inscribed angles. 5. Compare the measures. 1 What do you notice? 2 © 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia 3 4

© 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

© 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

• Construct a circle. • Select 2 points on the circle. Label them

• Construct a circle. • Select 2 points on the circle. Label them A and B. • Select a point P on the major arc. Construct the inscribed angle ∠APB. • Measure ∠APB with your protractor. Record the measure. A P © 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia B

• Select another point Q on the major arc. Construct the inscribed angle

• Select another point Q on the major arc. Construct the inscribed angle ∠AQB. • Measure ∠AQB with your protractor. Record the measure. • What do you notice? A B P Q © 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

© 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

© 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

1) Draw a circle. 2) Draw a central angle. 3) Measure of your central

1) Draw a circle. 2) Draw a central angle. 3) Measure of your central angle. 4) What is the relationship between the central angle and its intercepted arc? The two measurements will be equal. 5) Using the endpoints of the intercepted arc, draw two chords that intersect at a point on the circle but not on the intercepted arc. © 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

7) Make a prediction about the measure of the inscribed angle. 8) Measure the

7) Make a prediction about the measure of the inscribed angle. 8) Measure the inscribed angle. It should be ½ the measure of the central angle. 9) Write a comparison about your predicted and actual measurements of the two angles. 10) Compare your data with your partner. © 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

© 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

© 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

1. Explain why m∠ 1 = m∠ 2 + m∠ 3. Exterior Angle Theorem

1. Explain why m∠ 1 = m∠ 2 + m∠ 3. Exterior Angle Theorem A ∠ 2 ∠ 1 D B C ∠ 3 E 2. What do we know about m∠DCE and m∠ACB? They are ≅. (Vertical ∠s) © 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

1. Draw a circle. 2. Choose point C in the interior of the circle.

1. Draw a circle. 2. Choose point C in the interior of the circle. A B ∠ 1 D C E 3. Draw 2 chords that intersect at C. 4. Label A, B, D, E, and ∠ 1 as shown. © 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

5. Draw AD and label ∠ 2 and ∠ 3. A ∠ 2 ∠

5. Draw AD and label ∠ 2 and ∠ 3. A ∠ 2 ∠ 1 D B C ∠ 3 E © 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

3. Write an equation for the m∠ 2. ( A ∠ 2 m∠ 2

3. Write an equation for the m∠ 2. ( A ∠ 2 m∠ 2 = ½(ED) 4. Write an equation for the m∠ 3. ∠ 1 D B C ∠ 3 ( E m∠ 3 = ½(AB) ( ( 5. Write an equation for the m∠ 1. ( ( m∠ 1 = ½(ED) + ½(AB) = ½(ED + AB) © 2009, Dr. Jennifer L. Bell, La. Grange High School, La. Grange, Georgia

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