1. 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?

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

3. 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

4. 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

5. 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

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

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

8. 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

9. This also works for a radius!B Z D

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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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?