1. Unit 9 Standard 9a Arcs and Chords Learning Target: I can use properties of arcs and chords of a circle to find measurements.

2. Vocabulary for Circles There are 360° in a circle!! Central angle – In a plane, an angle whose vertex is the center of a circle. Arcs – Part of the circle that is measured by the central angle. Minor Arc – Measures less than 180° (typically named with 2 letters) Major Arc – Measures more than 180° (typically named with 3 letters) Semicircle – Measures exactly 180° P C A B AB ACB 45°

3. Measuring Arcs EF is the diameter of ʘ H. 1.Find the mGF. 2.Find the mGEF. 3.Find the mEF. 4.Find the mEG. 5.Find the m EHG. 60 o E H G F 60° = 300° 180° = 120° 120° 360 – 60 180 – 60

4. Arc Addition Postulate The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. mEGF=mEG+mGF E H G F

5. Example 1 = 148° = 148 + 180 = 180° A is the center of the circle (indicated by the point). = 328°

6. Example 2 A is the center of the circle (indicated by the point). = 60 + 82= 142° = 360 – 142= 218° = 218 – 100= 118°

7. Example 3 Find the mXY and mWZ. Are the measure of the arcs congruent? 65 ° mXY = 65° mWZ = 65° Yes!

8. Example 4 Find the measure of each arc. a. b. c. 40 ° 80 ° 110 ° NOTE: The arc measurement is in DEGREES!!! = 40 + 80= 120° = 40 + 80 + 110 = 230° = 360 – 230= 130°

9. Chord Chord - A segment whose endpoints are on the circle.

10. Chord Theorem In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. AB BC if and only if AB BC C A B

11. 2x ° (x + 40) ° D Example 5 Find the arc measure of AD. 2x = x + 40 x = 40 AD = 2(40) = 80

12. Assignment: 10.2 Practice B #1-21 only (This looks like a lot, but the questions are simpler.)