Transcript Geo Ch 10-2 – Arcs and Chords
Arcs and Chords
Chapter 10-2
• Recognize major arcs, minor arcs, semicircles, and central angles and their measures.
• Find arc length.
• central angle • arc • minor arc • major arc • semicircle
Standard 7.0
Students prove and use theorems involving
the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and t
he properties of circles.
(Key)
Central Angle
• An angle whose vertex B is the center of the circle • The sum of the central angles of a circle = 360 o Central C – As long as they don’t overlap Angle A BCA is a Central Angle
A.
9 B.
21 C.
65 D.
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A
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15 B.
25 C.
40 D.
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Arcs Def: A portion of a circle cut by two radii • Minor Arc—an arc formed by the interior of two radii with a central angle less than 180 o • Major Arc—an arc formed by the exterior of two radii with a central angle less than 180 o • Semi-Circle—an arc formed by the endpoints of a diameter • The measure of an arc is equal to the measure of the central angle that forms it
Animation: Arcs of a Circle
• Two arcs are if and only if their corresponding central angles are . (in the same circle or circles)
m AB = 60 ° B
Minor Arc
A 60 ° P m ADB = 300 ° D
Major Arc
Find the arc measures
B D A
45 ° 80 55 ° 45
C E
m AB = 80 ° m DE = 45 ° m AF = 45 ° m DF = 180 ° m BF = 125 ° m BD = 55 ° m DFB = 305 ° m FE = 135 °
F
Arc Addition
• The measure of an arc formed by two adjacent arcs is the sum of the measures of the 2 arcs B m CA = 40 ° A C m DC = 32 ° D m CA + m DC = 72 ° m DA = 72 °
Arc Addition Sample Problem
• Find m ABD m CA + m DC = m AD = m ABD 4x + 7 + 2x + 5 = 8x B 8x ° A m AC = 4x + 7 ° C m CD = 2x + 5 ° 6x + 12 = 8x 12 = 2x 6 = x m ABD m ABD = 8(6) = 48 ° D
Measures of Arcs
46 o
Measures of Arcs
is a minor arc, so is a semicircle.
46 o
Answer:
90
Measures of Arcs
46 o
Answer:
67
Measures of Arcs
46 o 44 o 46 o
Answer:
316
A.
54 B.
27 C.
108 D.
72
1.
2.
3.
4.
A B C D
A B C D
A.
54 B.
126 C.
108 D.
72
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2.
3.
4.
A B C D
A B C D
A.
126 B.
234 C.
180 D.
288
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2.
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4.
A B C D
A B C D
Circle Graphs A. BICYCLES This graph shows the percent of each type of bicycle sold in the United States in 2001. Find the measurement of the central angle representing each category.
Circle Graphs B. BICYCLES This graph shows the percent of each type of bicycle sold in the United States in 2001. Is the arc for the wedge named Youth congruent to the arc for the combined wedges named Other and Comfort? Answer:
no
Arc Length
• Arc length is a part of the circumference of a circle.
Arc length 2
r of AB
mAB
360
OR
Arc Length of AB
mAB
2
r
360
Find the Arc Length of AB
m
AB = 60 o r = 12 cm A B Arc Length of AB
mAB
2
r
360 Arc Length of AB 60 360 2 ( 12) Arc Length Arc Length of AB of AB 1 6 4 24 1 2 .
57 cm
Arc Length
In and . Write a proportion to compare each part to its whole.
Arc Length
degree measure of arc degree measure of whole circle Now solve the proportion for . arc length circumference Multiply each side by 9 .
Simplify.
Answer:
The length of is π units or about 3.14 units.
A.
7.88
B.
15.75
C.
49.48
D.
24.74
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Homework
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