B mAIsmacmathgeometry.weebly.com/uploads/1/9/2/5/... · Circles – Central Angles G.C.A.2 Notes...
Transcript of B mAIsmacmathgeometry.weebly.com/uploads/1/9/2/5/... · Circles – Central Angles G.C.A.2 Notes...
Circles – Central Angles G.C.A.2 Notes Section 12.3 Name__________________
Geometry Page 1 of 2
Arc: an unbroken part of a circle. x Minor Arc: an arc that measures less than 180. x Major Arc: an arc that measures more than 180. x Semicircle: an arc that measures 180.
Name each of the following from the picture.
Minor Arc Major Arc Semicircle Arc Length (Distance) & Arc Angle (Angle Measure)
Adjacent Arcs: arcs of a circle that have exactly one point in common.
Arc Measure: the measure of a arc is the measure of its central angle. The measure of a semicircle is 180.
Arc Addition Postulate: The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. Theorem 12.1: In the same (or in congruent) circle, two arcs are congruent IFF their corresponding central angles are congruent. Central angle of a regular polygon.
𝑚∠𝐶 =360𝑛
where n is the number of sides and ∠𝐶 is the central angle.
H
G
M
I
ED
F
H
G
M
I
H
G
M
I
H
G
M
I
B
A C
xC
HIandGI are adjacentMinorArc MajorArc
MI MI nai MAIHI MI
semicircleGMATGIH
O mLABCmAI 400G
40
mGMtmMH mGmH
FD FDE FDGn nDe DEF FEGEF J
B CE
ALICHELGCK iffJit7Gt
K
Length Angle measure
C 2rit MATT 900suoitat cm
ughAI Gotan m 364Gatcm 3
lengthFB sit cm mic 120
Circles – Central Angles G.C.A.2 Notes Section 12.3 Name__________________
Geometry Page 2 of 2
Complete each equation.
𝑚𝐶𝐸 = 𝑚𝐸𝐹 = 𝑚𝐸𝐶𝐾 = 𝑚𝐷𝐹𝐶 =
𝑚𝐴𝐶 = 𝑚𝐴𝐸 = 𝑚𝐸𝐾 = 𝑚∠𝐾𝐵𝐷 =
Given a regular polygon, complete each equation.
𝑚∠𝐴𝑇𝐵 = 𝑚∠𝐷𝑇𝐵 = 𝑚𝐴𝐶 = 𝑚𝐸𝐶𝐴 = 𝑚∠𝐴𝐸𝐵 = If 𝐴𝐵 = 5 cm, what does 𝑇𝐵 = If 𝐴𝐵 = 5 cm, what does 𝐸𝐴 =
34°
53°
H
K
F
A
C
D
E
70°
39°
K
E
B
A
CD
A
F
E
D
CT
B
A
F
E
D
CT
B
93 607 Ceo mLT 3
n
yo www.wj.noo mWao Ceo6
Y 60CeoCeo Ceo
tDE 93 GO 12053 13487
207 3600 530 120 240
3070
I 30 S141
iia SB39
39180 30,5
o 2.539 141 dkoa sonsSso g710 3A