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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Wrap up Cyclic QL Proof Warm-up Lesson: Cyclic Polygons Homework / Questions Clean-up. Warm-up – 2 minutes. Points B, C, D, and E all lie on Circle A. Find: mBC D E. What polygons are always cyclic? Triangles Quadrilaterals

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Wrap up Cyclic QL Proof • Warm-up • Lesson: Cyclic Polygons • Homework / Questions • Clean-up

  3. Warm-up – 2 minutes • Points B, C, D, and E all lie on Circle A. • Find: • mBC • D • E

  4. What polygons are always cyclic? • Triangles • Quadrilaterals • Squares? • Other rectangles? • Other rhombi? • Other parallelograms? • Trapezoids? • Other quadrilaterals? • Other polygons?

  5. Regular Polygons • A regular polygon is one that is convex, equilateral, and equiangular.

  6. Regular Polygons center • Important features: • n = number of sides • r = radius • a = apothem • s = side length

  7. Regular Polygons • Find the area of a regular polygon with n = 4 and r = 2. • n = 5and r = 2.

  8. Solutions 4 22 • n = 4, r = 2: • Square with diagonal = 4 • Side length = 4⁄2(by 45°-45°-90°) = 42⁄2 = 22 • Area = (side length)2 = 8 • n = 5, r = 2: • Need the apothem & side length. • x = 360°⁄10 = 36° • a = 2 cos x = 2 cos 36°  1.618 • s = 2(2 sin x) = 4 sin 36°  2.351 • Big triangle’s area = ½ as  1.902 • Pentagon area = 5(big triangle area)  9.51 x 2 a s

  9. Homework • Asg #85: • From Ch. 13, Lesson 1 (pp. 530-535): • Easy: 1-14. Med/hard: 46-47. • From Ch. 13, Lesson 2 (pp. 537-539): • Easy: 1-2, 6-12. Med: 29-31. • Bonus: Set III from Ch. 13, Lesson 1. • Due Friday, 6/7. • Final Exam Study Guide • Due the day of the final.

  10. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!

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