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Essential Circle Vocabulary: Angles, Arcs, and Congruency Explained

This resource covers fundamental terms related to circle geometry, including central angles, minor and major arcs, and semicircles. Essential concepts like the Arc Addition Postulate are explained, along with practical examples for finding indicated arc measures. Additional focus is given to congruency in circles and arcs, providing clarity on when circles and arcs are considered congruent. Ideal for students and educators looking to deepen their understanding of circle measures and properties.

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Essential Circle Vocabulary: Angles, Arcs, and Congruency Explained

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Presentation Transcript

  1. Find Arc measures 10.2

  2. Vocab • Central Angle: an angle where the vertex is at the center of the circle.

  3. And the vocab continues • Minor arc: an angle inside a circle whose measure is less than 180°. (They only need 2 letters to be named but can also have 3 letters.) • Major arc: an angle inside a circle whose measure is greater than 180° or the arc that is not the minor arc. (They require 3 letters to be named) • Semicircle: • Half a circle

  4. Name the minor and major arc I’m a minor! I’m a major!

  5. Arc Addition postulate This theorem allows us to add arcs

  6. Find the indicated arc

  7. Find the indicated arc 360 – 90 = 270º

  8. Find the indicated arc 360 ÷3 = 120º

  9. Finding measures of arcs, where EB is a diameter 75º 180-35 = 145º 75o 75 + 35 = 110º 35o 360 – 110 = 250º

  10. Word Problems 306o B 306 c 360 – 306 = 54º 180 +54 = 234º A 54º 180º D

  11. Congruency • Circles are said to be congruent if and only if their radii are the same. • Arcs are considered to be congruent if they are the same measure and the circles they are contained in are also congruent. • 2 arcs of the same measure in the same circle are considered congruent.

  12. Congruent?

  13. Congruent?

  14. You try • Page 661 3-14, 17, 24a-b

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