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Section 6.3 Applying Properties of Chords

Section 6.3 Applying Properties of Chords. Tell whether the segment is best described as a radius, chord, or diameter of C. 1. DC. radius. ANSWER. Warm up for Lesson 6.3. Tell whether the segment is best described as a radius, chord, or diameter of C. 2. BD. diameter. ANSWER.

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Section 6.3 Applying Properties of Chords

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  1. Section 6.3Applying Properties of Chords

  2. Tell whether the segment is best described as a radius, chord, or diameter of C. 1.DC radius ANSWER Warm up for Lesson 6.3

  3. Tell whether the segment is best described as a radius, chord, or diameter of C. 2.BD diameter ANSWER Warm up for Lesson 6.3

  4. Tell whether the segment is best described as a radius, chord, or diameter of C. 3.DE chord ANSWER Warm up for Lesson 6.3

  5. Tell whether the segment is best described as a radius, chord, or diameter of C. 4.AE chord ANSWER Warm up for Lesson 6.3

  6. Theorem 6.5

  7. Theorem 6.6

  8. Theorem 6.7

  9. Theorem 6.8

  10. In the diagram, PQ, FGJK, and mJK= 80o. Find mFG Because FGand JKare congruent chords in congruent circles, the corresponding minor arcs FGand JKare congruent. So, mFG = mJK = 80o. EXAMPLE 1 Use congruent chords to find an arc measure SOLUTION

  11. Use the diagram of D. ANSWER 1. If mAB= 110°, find mBC mBC = 110° for Example 1 GUIDED PRACTICE

  12. Use the diagram of D. ANSWER 2. If mAC = 150°, find mAB mAB = 105° for Example 1 GUIDED PRACTICE

  13. Gardening Three bushes are arranged in a garden as shown. Where should you place a sprinkler so that it is the same distance from each bush? Label the bushes A, B, and C, as shown. Draw segments ABand BC. STEP 1 EXAMPLE 2 Use perpendicular bisectors SOLUTION

  14. Draw the perpendicular bisectors of ABand BCBy Theorem 10.4, these are diameters of the circle containing A, B, and C. STEP 2 STEP 3 Find the point where these bisectors intersect. This is the center of the circle through A, B, and C, and so it is equidistant from each point. EXAMPLE 2 Use perpendicular bisectors

  15. Use the diagram of Eto find the length of AC. Tell what theorem you use. ANSWER Diameter BDis perpendicular to AC. So, by Theorem 10.5, BDbisects AC, and CF = AF. Therefore, AC = 2 AF =2(7) = 14. EXAMPLE 3 Use a diameter

  16. Find the measure of the indicated arc in the diagram. 3. CD ANSWER mCD=72° for Examples 2 and 3 GUIDED PRACTICE

  17. Find the measure of the indicated arc in the diagram. 4. DE mCD=mDE. ANSWER mDE=72° 5. CE mCE=mDE + mCD mCE=72°+ 72° = 144° ANSWER for Examples 2 and 3 GUIDED PRACTICE

  18. In the diagram of C, QR = ST = 16. Find CU. Chords QRand STare congruent, so by Theorem 10.6 they are equidistant from C. Therefore, CU = CV. Use Theorem 6.8 EXAMPLE 4 SOLUTION CU = CV Use Theorem 6.8 2x = 5x – 9 Substitute. Solve for x. x = 3 So, CU = 2x = 2(3) = 6.

  19. In the diagram in Example 4, suppose ST = 32, and CU= CV = 12. Find the given length. ANSWER QR= 32 for Example 4 GUIDED PRACTICE 6. QR

  20. In the diagram in Example 4, suppose ST = 32, and CU= CV = 12. Find the given length. ANSWER QU= 16 for Example 4 GUIDED PRACTICE 7. QU

  21. In the diagram in Example 4, suppose ST = 32, and CU= CV = 12. Find the given length. 8. The radius of C ANSWER The radius of C = 20 for Example 4 GUIDED PRACTICE

  22. Find the value of x in C. Explain. . 1. ANSWER 6; If a diameter of a circle is to the chord, then the diameter bisects the chord and its arc. Daily Homework Quiz For use after Lesson 10.3

  23. ~ Find the value of x in C. Explain. = . ANSWER 4; In the same circle, if two chords are equidistant from the center, then they are . Daily Homework Quiz For use after Lesson 10.3 2.

  24. Determine whether RS is a diameter. ANSWER Yes. Sample answer: RS is the bisector of TU by Theorem 5.3. Then RS is a diameter of the circle by Theorem 10.4. Daily Homework Quiz For use after Lesson 10.3 3.

  25. Homework page 201 (1-13 odd)page 203 (5-15 odd, 16-22 all)

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