1 / 17

Exploring Inscribed Angles & Arcs in Circles Activity

Engage in geometry investigation on inscribed angles, intercepted arcs, and the relationships within circles. Analyze angles RTS, RUS, RVS, compare angles, and apply theorems and practices in circle geometry.

philander-steve
Télécharger la présentation

Exploring Inscribed Angles & Arcs in Circles Activity

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related