1. Over Lesson 10–2 A.A B.B C.C D.D 5-Minute Check 1 114

2. Over Lesson 10–2 A.A B.B C.C D.D 5-Minute Check 2 66

3. Over Lesson 10–2 A.A B.B C.C D.D 5-Minute Check 3 125

4. Over Lesson 10–2 A.A B.B C.C D.D 5-Minute Check 4 150

5. Over Lesson 10–2 A.A B.B C.C D.D 5-Minute Check 5 210

6. Over Lesson 10–2 A.A B.B C.C D.D 5-Minute Check 6 A.129.6 ft B.165 ft C.259.2 ft D.345.6 ft Dianne runs around a circular track that has a radius of 55 feet. After running three quarters of the distance around the track, how far has she run?

7. Then/Now Recognize and use relationships between arcs and chords. Recognize and use relationships between arcs, chords, and diameters.

8. Concept

10. Example 1 Use Congruent Chords to Find Arc Measure Jewelry A circular piece of jade is hung from a chain by two wires around the stone. JM  KL and = 90. Find.

11. Example 1 Use Congruent Chords to Find Arc Measure

12. A.A B.B C.C D.D Example 1 85

13. Example 2 Use Congruent Arcs to Find Chord Lengths

14. Example 2 Use Congruent Arcs to Find Chord Lengths WX= YZDefinition of congruent segments 7x – 2= 5x + 6Substitution 2x= 8Add 2 to each side. x= 4Divide each side by 2. So, WX = 7x – 2 = 7(4) – 2 or 26. Answer: WX = 26

15. A.A B.B C.C D.D Example 2 13

16. Concept

17. Example 3 Use a Radius Perpendicular to a Chord Answer:

18. A.A B.B C.C D.D Example 3 80

19. Example 4 Use a Diameter Perpendicular to a Chord CERAMIC TILE In the ceramic stepping stone below, diameter AB is 18 inches long and chord EF is 8 inches long. Find CD.

20. Example 4 Use a Diameter Perpendicular to a Chord Step 1Draw radius CE. This forms right ΔCDE.

21. Example 4 Use a Diameter Perpendicular to a Chord Step 2Find CE and DE. Since AB = 18 inches, CB = 9 inches. All radii of a circle are congruent, so CE = 9 inches. Since diameter AB is perpendicular to EF, AB bisects chord EF by Theorem 10.3. So, DE = (8) or 4 inches. __ 1 2

22. Example 4 Use a Diameter Perpendicular to a Chord Step 3Use the Pythagorean Theorem to find CD. CD 2 + DE 2 = CE 2 Pythagorean Theorem CD 2 + 4 2 = 9 2 Substitution CD 2 + 16= 81Simplify. CD 2 = 65Subtract 16 from each side. Take the positive square root. Answer:

23. A.A B.B C.C D.D Example 4 4.90 In the circle below, diameter QS is 14 inches long and chord RT is 10 inches long. Find VU to the nearest hundredth.

24. Concept

25. Example 5 Chords Equidistant from Center Since chords EF and GH are congruent, they are equidistant from P. So, PQ = PR.

26. Example 5 Chords Equidistant from Center PQ= PR 4x – 3= 2x + 3Substitution x= 3Simplify. So, PQ = 4(3) – 3 or 9 Answer: PQ = 9

27. A.A B.B C.C D.D Example 5 15