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Lesson 9-4 Arcs and Chords (page 344) Essential Question How can relationships in a circle allow you to solve problems involving arcs and chords?
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Arcs & Chords Z X Y The minor arc, _________ is the arc of chord _________.
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In the same circle or in congruent circles: (1) congruent arcs have congruent chords, (2) congruent chords have congruent arcs. Theorem 9-4 R T U S O
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In the same circle or in congruent circles: (1) congruent arcs have congruent chords, Theorem 9-4 R T U S O Prove congruent triangles by using the SAS Postulate, then use CPCTC.
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In the same circle or in congruent circles: (2) congruent chords have congruent arcs. Theorem 9-4 R T U S Q Prove congruent triangles by using the SSS Postulate, then use CPCTC and Theorem 9-3.
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A point Y is called the midpoint of … Y ZX
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A diameter that is perpendicular to a chord bisects the chord and its arc. Theorem 9-5 Z C O D BA
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A diameter that is perpendicular to a chord bisects the chord and its arc. Theorem 9-5 Z C O D BA Prove congruent triangles by using the HL Theorem, then use CPCTC for each prove and Theorem 9-3.
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This also works for a radius! Z O D BA
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HEY! CHECK THIS OUT! Yes, it even works here! Z O BA Math is so COOL!
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In the same circle or in congruent circles: (1) chords equally distant from the center(s) are congruent, (2) congruent chords are equally distant from the center(s). Theorem 9-6 B A D C O X Y
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In the same circle or in congruent circles, (1) chords equally distant from the center(s) are congruent, Theorem 9-6 B A D C O X Y Prove congruent triangles by using the HL Theorem, then use CPCTC and Theorem 9-5.
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In the same circle or in congruent circles, (2) congruent chords are equally distant from the center(s). Theorem 9-6 B A D C Q X Y Use Theorem 9-5 to help prove congruent triangles by using the HL Theorem, then use CPCTC.
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Q 70º R P S Example #1 If PS = 12 and TR = 15, then find QR. QR = _______. 12 60º 50º T 20º 160º 12 15
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Example #2 In A, SQ = 12 and AT = 8, then find PR. PR = _______. 20 10 66 T P A R QS 8
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Example #3 In O, FL = 3, GO = 5, and OP = 4, then find HJ. HJ = _______. 6 3 5 P G O F JH 4 L 3 4 6
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Assignment Written Exercises on page 347 GRADED: 1 to 9 odd numbers How can relationships in a circle allow you to solve problems involving arcs and chords?
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