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Geometry

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  1. Geometry 9.4 Arcs and Chords

  2. Theorem • In the same circle or in congruent circles: • congruent arcs have congruent chords • congruent chords have congruent arcs ● O

  3. 130 110 Y 22 P Q X 10 Z 15 W U 8 12 V R Exercises 110 2. 1. 110 130 140 115

  4. Theorem A diameter that is perpendicular to a chord bisects the chord and its arc. ● O

  5. K A H G J Q Q B Q 12 6 D F M C E Exercises 4 3 200˚ 3. 4. 5. 12 5 80

  6. Theorem • In the same circle or in congruent circles: • chords equally distant from the center (or centers) are congruent • congruent chords are equally distant from the center (or centers) ● O

  7. Q F A B 6 Y 8 S 9 18 C O P O X K O 8 O R E M T H G D N Exercises 12√2 6 9√3 6√2 6 12√2 11. 10. 9. 12 DC = ____ 18√3 6√2

  8. Exercise (like on your homework) • Sketch a circle O with radius length 17 and a chord • that has a length 30. How far is the chord from O? A 17 17 15 ● O Pythag. Triple 8-15-17 30 8 B The chord is 8 units from circle O.

  9. Exercise (like on your homework) 13. Sketch a circle R with radius length 5√3 and a chord that is 5 units from R. Find XY. 5√3 Pythag. Thm: 5²+x²= (5√3)² x² + 25 = 75 x² = 50 x = 5√2 2 ● 5√2 = 10√2 R Y 5√3 ● x 5 X Chord XY is 10√2 units long.

  10. Homework pg. 346 CE #1-5 WE # 1-13 Quiz Friday

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