1. 10.3 Apply Properties of Chords Hubarth Geometry

2. Theorem 10.3 In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. A B C D

3. In the diagram, P Q, FG JK, and mJK = 80 o. Find mFG Because FG and JK are congruent chords in congruent circles, the corresponding minor arcs FG and JK are congruent. So, mFG = mJK = 80 o. Ex 1 Use Congruent Chords to Find an Arc Measures

4. Theorem 10.4. J M P K L

5. Theorem 10.5. B F E D G

6. Use the diagram of E to find the length of AC. Tell what theorem you use. Diameter BD is perpendicular to AC. So, by Theorem 10.5, BD bisects AC, and CF = AF. Therefore, AC = 2 AF = 2(7) = 14. Ex 2 Use a Diameter

7. Theorem 10.6 In the same circle, or in congruent circles. two chords are congruent if and only if they are equidistant from the center.. A B C D G F E

8. Ex 3 Use Theorem 10.6 Chords QR and ST are congruent, so by Theorem 10.6 they are equidistant from C. Therefore, CU = CV. CU = CV 2x = 5x – 9 x = 3 So, CU = 2x = 2(3) = 6. In the diagram of C, QR = ST = 16. Find CU.

9. Practice Use the diagram of D. 1. If mAB = 110 °, find mBC mBC = 110 ° 2. If mAC = 150 °, find mAB mAB = 105 ° Find the measure of the indicated arc. 3. CD 4. DE 5. CE mCD = 72° mDE = 72° mCE = 72° + 72° = 144° Find the given length 6. QR 7. QU 8. The radius of circle C 32 16 r = 20