10.2 measuring angles and arcs 2016 ink.notebook
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March 15, 2017
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10.2
Measuring
Angles
and Arcs
Page 97
Page 98
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10.2 measuring angles and arcs 2016 ink.notebook
Lesson Objectives
Standards
March 15, 2017
Lesson Notes
Standards
Lesson Objectives
10.2 Measuring Angles and Arcs
Lesson Notes
After this lesson, you should be able to successfully use angle measures to find arc measures.
Press the tabs to view details.
Press the tabs to view details.
Lesson Objectives
Standards
Lesson Notes
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.C.2 Identify and describe relationships among inscribed angles, radii, and chords.
Chord that passes through the center of the circle.
DIAMETER
DIAMETER = 2 x Radius
You will know it's a diameter
if there's a dot ON the line!
NOT a
diameter
All radii are congruent
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10.2 measuring angles and arcs 2016 ink.notebook
March 15, 2017
Angles and Arcs ­ A __________________ is an angle whose vertex is at the center of a circle and whose sides are radii. A central angle separates a circle into two arcs, a ________________ arc and a _____________ arc.
C
E
H
F
Ce
An ntr
gl al
e
G
Major Arc > 180
> 180
semicircle = 180
SE
An angle whose VERTEX is at the center and whose SIDES are radii of the circle.
Measure of the
central angle =
measure of the
intercepted arc
SEMICIRCLES are congruent arcs
formed when the diameter of a circle separates the circles into two arcs.
M
I C I RC
LE
Minor Arc < 180
< 180
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10.2 measuring angles and arcs 2016 ink.notebook
March 15, 2017
C
Here are some properties of H
central angles and arcs.
measure of central angle = measure minor arc
E
F
G
The sum of the measures of the central angles of a circle with no interior points in common is 360.
mÚHEC + mÚCEF + mÚFEH + mÚGEH = 360
The measure of a minor arc is less than 180 and equal to the measure of its central angle.
C
E
H
F
G
The measure of a major arc is 360 minus the measure of the minor arc.
The measure of a semicircle is 180.
D
= 180
A
O
B
C
Two minor arcs are congruent if and only if their if and only if corresponding central angles are congruent.
ÚCEF ¤ ÚFEG
C
E
H
F
G
The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. (Arc Addition Postulate)
2.
3.
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10.2 measuring angles and arcs 2016 ink.notebook
March 15, 2017
Identify each arc as a major arc, minor arc, or a semicircle of the circle. Then find its measure.
Arc Length ­ An ARC is part of a circle and its length is a part of the circumference of the circle.
The length of arc  can be found using the following equation. Round to the nearest hundredth.
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10.2 measuring angles and arcs 2016 ink.notebook
March 15, 2017
Use ËO to find the length of each arc. Round to the nearest hundredth.
Arc LENGTH
Â
=
x
(2)(3.14)r
360
Use ËP to find the length of each arc. Round to the nearest hundredth.
S
15.
50
50
M
16.
N
T
R
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10.2 measuring angles and arcs 2016 ink.notebook
Use ËP to find the length of each arc. Round to the nearest hundredth.
March 15, 2017
S
17.
50
50
M
18.
N
T
P
R
19. PIES Yolanda has divided a circular apple pie into 4 slices by cutting the pie along 4 radii. The central angles of the 4 slices are 3x, 6x − 10, 4x + 10, and 5x degrees. What exactly are the numerical measures of the central angles?
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10.2 measuring angles and arcs 2016 ink.notebook
March 15, 2017
HOMEWORK
10.2 Practice on Measuring Angles and Arcs
On the
Worksheet
are diameters of ËR. Identify each arc as a
major arc, minor arc, or a semicircle of the circle. Then find its measure.
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10.2 measuring angles and arcs 2016 ink.notebook
March 15, 2017
Use ËD to find the length of each arc. Round to the nearest hundredth.
Use ËD to find the length of each arc. Round to the nearest hundredth.
21. HOMEWORK Refer to the table, which shows the number of hours students at Leland High School say they spend on homework each night.
a) If you were to construct a circle graph of the data, how many degrees would be allotted to each category?
b) Describe the arcs associated with each category. (major, minor, etc.)
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10.2 measuring angles and arcs 2016 ink.notebook
22. CONDIMENTS A number of people in a park were asked to name their favorite condiment for hot dogs. The results are shown in the circle graph.
What percent named each as their favorite condiment?
March 15, 2017
23. BIKE WHEELS Lucy has to buy a new wheel for her bike. The bike wheel has a diameter of 20 inches.
a) If Lucy rolls the wheel one complete rotation along the ground, how far will the wheel travel? Round your answer to the nearest hundredth of an inch.
b) If the bike wheel is rolled along the ground so that it rotates 45, how far will the wheel travel? Round your answer to the nearest hundredth of an inch.
c) If the bike wheel is rolled along the ground for 10 inches, through what angle does the wheel rotate? Round your answer to the nearest tenth of a degree. 24. Solve by SUBSTITUTION.
Think BOX. Show all work.
25. Solve by MULTIPLYING first, then adding. Show all work.
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10.2 measuring angles and arcs 2016 ink.notebook
26. Solve by MULTIPLYING first, then adding. Show all work.
March 15, 2017
Answers:
1. minor, 50 3. minor 100 5. minor 130 7. 130 9. 90 11. 140 13. 230 15. 8.72 in 17. 7.33 cm 19. 25.12 mm 21.a) 28.8, 104.4, 208.8, 10.8, 7.2 21.b) minor, minor, major, minor, minor 23a) 62.8 in b) 7.85 in c) 57.3¡ 25. (2, –2)
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