GEOMETRYCharacter builds slowly, but it can be torn down with incredible swiftness.

Faith Baldwin

Today:10.3 InstructionPractice

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

GEOMETRY

10.3 - ARCS AND CHORDS

Objectives: Know and use relationships between arcs

and chords Know and use properties of chords of

circles

Vocabulary: congruent arcs

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.

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.

radiu

sdiameter

chord

secant

tangent

center

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

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

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

60°A

B

C

D

In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

ABCD if and only if ABCD

A

B

C

D

Find mCD.

4x°

E

D

C

x + 78°

B

If a diameter or radius of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

DEEF, DGGF

F

G

E

D

OIf OG is a diameter of circle O, then

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

BABCD if and only if EFEG

D

G

What happens if the segment is also perpendicular?

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

AB = 12, DE =12, and CG = 7. Find CEF.

E

D

C

B

G

A

F

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.

Character builds slowly, but it can be torn down with incredible swiftness.

Faith Baldwin

Assignment:10.3 p 718 #1-13

Odd, 20, 45, 47Quiz 10.1-10.5

Friday

GEOMETRY