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Chapter 7 – Circles

Chapter 7 – Circles.

gary-lynch
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Chapter 7 – Circles

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  1. Chapter 7 – Circles In previous chapters, you have extensively studied triangles and quadrilaterals to learn more about their sides and angles. In this chapter, you will connect your understanding of polygons with your knowledge of the area ratios of similar figures to find the area and circumference of circles of all sizes. You will explore the relationships between angles, arcs, and chords in a circle. Then you will find the equation of a circle using the Pythagorean Theorem.

  2. 7.1 What If There Are No Sides? Pg. 4 Circumference and Arc Length

  3. 7.1 – What If There Are No Sides? Circumference and Arc Length In previous chapters you discovered the perimeter and area of polygons. Today you will discover how to find the perimeter of a shape with no sides, a circle.

  4. The set of all points in a plane that are equidistant from a given point

  5. Point equidistant from the sides of the circle. Gives the name of the circle. P

  6. A segment with endpoints at the center and on the circle Q P

  7. A segment with both endpoints on the circle that goes through the center of the circle Q P R

  8. 7.1 – RATIOS OF CIRCLES Find the measure of the circumference by wrapping a string around the entire perimeter of the circle and then measuring how long the string is in centimeters. Then estimate the diameter (length across the circle). Then write the ratio. What do you notice? What value are you finding?

  9. Length around a circle

  10. 7.3 – MISSING INFORMATION Using your understanding of the relationship between circumference (perimeter of a circle) and the diameter, find the missing values. a. Find the circumference of a circle with a diameter of 12 inches.

  11. c. Find the circumference of a circle with a radius of 16 inches. Leave answers in terms of pi.

  12. d. Michael noticed a pattern in the relationship between the radius, diameter, and circumference. Complete the table below. Be sure to leave pi in your answer when finding the circumference. 3 5 10 15 24 2r

  13. 7.4 – WHEELS GO ROUND AND ROUND Evelyn's in-line skate wheels have a 0.42m diameter. How many meters will Evelyn travel after 5000 revolutions of the wheels on her in-line skates?

  14. 7.5 – PERIMETER Find the perimeter of each shape. Leave answers in terms of pi.

  15. m

  16. 2 mm

  17. Part of a circle

  18. Arc Length: Length around part of a circle

  19. 7.6 – ARC LENGTH Find the part of the circumference that is between points A and B.

  20. 7.7 – ARC LENGTH Find the length of the shaded arc. Leave answers in terms of pi.

  21. http://www.youtube.com/watch?v=GmiXemW_oBQ

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