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### Understanding Circles: Parts, Circumference, and Formulas ###

This lesson provides a comprehensive overview of circles, including key definitions and relationships between their parts. A circle is defined as a plane figure with all points equidistant from a central point known as the center. Key components such as radius and diameter are discussed, alongside the mathematical relationships that define them. The circumference formulas, ( C = pi d ) and ( C = 2pi r ), allow for the calculation of a circle's circumference, with an emphasis on the constant pi (π). Engage in practice exercises to reinforce understanding. ###

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### Understanding Circles: Parts, Circumference, and Formulas ###

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  1. Circles and Circumference Lesson 10-2

  2. Vocabulary • A circle is a plane figure that consists of a set of points that are equidistant from a given point called the center. • The circumference of a circle is the distance around it.

  3. Identifying the Parts of a Circle A radius is a line segment that connects the outside of the circle to its center.

  4. A diameter is a line segment with both endpoints on the circle that passes through the center.

  5. Numerical Relationships • A radius is exactly one-half of a diameter. • Therefore a diameter is twice a radius. If the radius is 5.5 cm, then the diameter is ___________ cm. 11 5.5 cm

  6. Circumference Formulas C = πd C = 2πr

  7. Circumference • Remember, circumference is the distance around the circle. • If you divide a circle’s circumference by its diameter, you always get the same irrational number – pi (symbol: π) • This is true of every circle. • We estimate pi to be 3.14 or the fraction 22/7.

  8. Example C = πd C = (3.14)(41) 41 m C = 128.74 m We substitute 3.14 in for pi.

  9. Example C = 2πr C = (2)(3.14)(6) 6in C = 37.68in We substitute 3.14 in for pi.

  10. Practice Time P 531 # 2, 3, 5, 6, 8, 9

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