Lesson 9-4 Arcs and Chords (page 344) Essential Question How can relationships in a circle allow you to solve problems involving segments, angles, and arcs?

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

Theorem 9-4 In the same circle or in congruent circles: (1) congruent arcs have congruent chords , (2) congruent chords have congruent arcs . T R O U S

Theorem 9-4 In the same circle or in congruent circles: (1) congruent arcs have congruent chords , T R Prove congruent triangles by using the SAS Postulate, then use CPCTC. O U S

Theorem 9-4 In the same circle or in congruent circles: (2) congruent chords have congruent arcs . T R Prove congruent triangles by using the SSS Postulate, then use CPCTC and Theorem 9-3. Q U S

A point Y is called the midpoint of … X Z Y

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

Prove congruent triangles then use CPCTC for each prove Theorem 9-5 Prove congruent triangles by using the HL Theorem, then use CPCTC for each prove and Theorem 9-3. A diameter that is perpendicular to a chord bisects the chord and its arc. C O A B Z D

This also works for a radius! B Z D

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

Theorem 9-6 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). A X B O D Y C

Prove congruent triangles by using the HL Theorem, then In the same circle or in congruent circles, (1) chords equally distant from the center(s) are congruent , Prove congruent triangles by using the HL Theorem, then use CPCTC and Theorem 9-5. A X B O D Y C

Theorem 9-6 In the same circle or in congruent circles, (2) congruent chords are equally distant from the center(s). Use Theorem 9-5 to help prove congruent triangles by using the HL Theorem, then use CPCTC. A X B Q D Y C

If PS = 12 and TR = 15, then find QR. Example #1 If PS = 12 and TR = 15, then find QR. QR = _______. 12 60º R S 20º 15 70º T 12 50º Q P 160º

In A, SQ = 12 and AT = 8, then find PR. Example #2 In A, SQ = 12 and AT = 8, then find PR. PR = _______. 20 P A 10 8 T S Q 6 6 R

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

Assignment Written Exercises on pages 347 & 348 RECOMMENDED: 1 to 10 ALL numbers, 12 REQUIRED: 11, 13, 18, 20, 22, 25 Prepare for Quiz on Lessons 9-1 to 9-4 How can relationships in a circle allow you to solve problems involving segments, angles, and arcs?