1. G EOMETRY Character builds slowly, but it can be torn down with incredible swiftness. Faith Baldwin Today: 10.3 Instruction Practice

2. Character builds slowly, but it can be torn down with incredible swiftness. Faith Baldwin Assignment: 10.2 p 710 #7-9, 44-47, 59, 63-64 G EOMETRY

3. 10.3 - A RCS AND C HORDS Objectives: Know and use relationships between arcs and chords Know and use properties of chords of circles Vocabulary: congruent arcs

4. CCSS Content Standards G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Mathematical Practices 4 Model with mathematics. 3 Construct viable arguments and critique the reasoning of others.

5. Then/Now You used the relationships between arcs and angles to find measures. Recognize and use relationships between arcs and chords. Recognize and use relationships between arcs, chords, and diameters.

6. radius diameter chord secant tangent center

7. central angle minor arc – connects an angle under 180° major arc – connects an angle over 180° Named by two letters Named by three letters B C A D

8. congruent arcs: arcs of the same measure in either the same circle or congruent circles.

9. 60° A B C D

10. In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. AB  CD if and only if AB  CD A B C D

11. Find mCD. 4x° E D C x + 78° B

12. If a diameter or radius of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. DE  EF, DG  GF F G E D O If OG is a diameter of circle O, then

13. In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center. A F C B AB  CD if and only if EF  EG D G What happens if the segment is also perpendicular?

14. In Circle R, LM = NO, LM = 60, TR = 40 and mLM = 80. Find mNQ, TO and RM.

15. AB = 12, DE =12, and CG = 7. Find  CEF. E D C B G A F

16. Example 4 Use a Diameter Perpendicular to a Chord CERAMIC TILE In the ceramic stepping stone below, diameter AB is 18 inches long and chord EF is 8 inches long. Find CD.

17. Character builds slowly, but it can be torn down with incredible swiftness. Faith Baldwin Assignment: 10.3 p 718 #1-13 Odd, 20, 45, 47 Quiz 10.1-10.5 Friday G EOMETRY