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?

Arcs & Chords Z X Y The minor arc, _________ is the arc of chord _________.

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

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.

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.

A point Y is called the midpoint of … Y ZX

A diameter that is perpendicular to a chord bisects the chord and its arc. Theorem 9-5 Z C O D BA

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.

This also works for a radius! Z O D BA

HEY! CHECK THIS OUT! Yes, it even works here! Z O BA Math is so COOL!

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

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.

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.

Q 70º R P S Example #1 If PS = 12 and TR = 15, then find QR. QR = _______ º 50º T 20º 160º 12 15

Example #2 In  A, SQ = 12 and AT = 8, then find PR. PR = _______ T P A R QS 8

Example #3 In  O, FL = 3, GO = 5, and OP = 4, then find HJ. HJ = _______ P G O F JH 4 L 3 4 6

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?