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Geometry

Learn about the Arcs and Chords Theorem in geometry, including congruent arcs, congruent chords, and the properties of perpendicular diameters. Solve exercises involving chords and arcs, and apply the Pythagorean Theorem to find chord lengths.

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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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