Trigonometry - Quia



Geometry Lesson Notes 10.3 ____________________

Objective : Recognize and use the relationships between arcs and chords and between

chords and diameters.

Arc of a chord: an arc that shares the same endpoints as a chord.

Theorem: In a circle or congruent circles, two minor arcs are congruent if and only if

their corresponding chords are congruent.

Abbrev: If 2 minor arcs are ( , corr. chords are ( .

If 2 chords are ( , corr. minor arcs are ( .

Example:

If m(AJB = m(CJD and CD = 6 cm,

then AB = __________

Theorem: If a diameter (or radius) of a circle is perpendicular to a chord, then it bisects the

chord and its arc.

Example 3 (p 538): Radius Perpendicular to a Chord

If EG = 28 in, then FG = ___________

If m[pic] = 135(, then m[pic] = __________

If the radius of (A is 5 cm and

EG = 8 cm, then FH = __________

REMEMBER THIS STRATEGY!

Theorem: In a circle, two chords are congruent if and only if they are equidistant from the

center.

Remember, distances are perpendicular measures!

Example 4 (p 539): Chords Equidistant from Center

a. If QJ = QP, name the congruent arcs and

congruent segments.

If [pic], name all congruent segments

b. The radius of (Q is 17 cm and [pic].

If MN = 30 ft, find QP.

REMEMBER THIS STRATEGY!

DRAW A RADIUS TO

CREATE A RIGHT (.

Practice:

Given: (G has radius of 10

and DC = 10

DE = __________

m(DGE = __________

m[pic] = __________

m[pic] = __________

m[pic] = __________

Given: GJ = GK = BJ = 10

DC = __________

GE = __________

GB = __________

m(BGH = __________

m[pic] = __________

m[pic] = __________

USE THE STRATEGY!

( HW A3a pp 540-543 #11-35, 40, 42, 52, 53

A3b Lesson 10-3 Skills Practice / Practice

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Q

J

L

K

N

M

K

F

D

A

K

F

D

I

B

P

J

C

C

J

B

B

A

A

G

F

J

G

D

H

C

E

A

G

E

E

H

H

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