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Warm-Up

Warm-Up. Geometry. Inscribed Angles and Other Relationships. Vocabulary. Central Angle – an angle whose vertex is on the center of a circle. The arc measure is equal to the measure of the central angle. Inscribed Angle – an angle whose vertex is on a circle.

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Warm-Up

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  1. Warm-Up

  2. Geometry Inscribed Angles and Other Relationships

  3. Vocabulary • Central Angle – an angle whose vertex is on the center of a circle. The arc measure is equal to the measure of the central angle. • Inscribed Angle – an angle whose vertex is on a circle. • Intercepted Arc – the arc that lies between an inscribed angle.

  4. Investigation Activity • Use trace paper to create angles RTS, RUS, and RVS. • Compare the four angles to each other (RPS, RTS, RUS, RVS). What do you notice?

  5. Theorems

  6. Draw a right triangle in your circle.How do you know it is a right triangle? • Draw a quadrilateral in your circle. What can you conclude about the angles of your quadrilateral?

  7. Theorems

  8. Practice m∠BAC = = = 2 = m∠BAC = m∠BAC = m∠BAC =

  9. Practice 3y + 3x = 180° y + x = 60° y = 60° - x 2y + 5x = 180° 2(60°-x) +5x = 180° 120° -2x +5x = 180° 3x = 60° x = 20° 2x + 100° = 180° -100° -100° 2x = 80° x = 40 y + 87° = 180° -87° -87° y = 93° y =60° - 20° y =40°

  10. 10.4 – Other Relationships in Circles.

  11. Practice • Since the intersection occurs inside of the circle. We add the two intercepted arcs formed by the angle and its vertical angle.

  12. Practice • Since the intersection occurs outside of the circle. We subtract the arcs formed by the angle and then divide by two.

  13. Practice • Since the intersection occurs outside of the circle. We subtract the arcs formed by the angle and then divide by two.

  14. Practice

  15. Practice

  16. Exit Ticket Homework • Copy down one of the pictures and examples that we completed in class and turn it in. • Pg. 617: 9-23 odd • Pg. 624: 9-27 odd

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