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5-Minute Check on Lesson 10-15-Minute Check on Lesson 10-15-Minute Check on Lesson 10-15-Minute Check on Lesson 10-1 Transparency 10-2
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Refer to ⊙F.
1. Name a radius
2. Name a chord
3. Name a diameter
Refer to the figure and find each measure
4. BC
5. DE
6. Which segment in ⊙C is a diameter?Standardized Test Practice:
A CB DAC CD CB AB
FL, FM, FN, FO
LN, MO, MN, LO
LN, MO
3
13
D
D
AC
B
Lesson 10-2
Angles and Arcs
Objectives
• Recognize major arcs, minor arcs, semicircles, and central angles and their measures– central angles sum to 360°– major arcs measure > 180°– minor arcs measure < 180°– semi-circles measure = 180°
• Find arc length– Formula: C • (central angle / 360°)
% of circle that is the arc
Vocabulary
• Central Angle – has the center of the circle as its vertex and two radii as sides
• Arc – edge of the circle defined by a central angle
• Minor Arc – an arc with the central angle less than 180° in measurement
• Major Arc – an arc with the central angle greater than 180° in measurement
• Semicircle – an arc with the central angle equal to 180° in measurement
• Arc Length – part of the circumference of the circle corresponding to the arc
Circles - Arcsy
x
Central
Angle
Diameter (d)
Center
B
GF
E
H
BHG
BEG
Semi-CircleEHF
Circles - Probabilityy
xRadius (r)
Diameter (d)
Center
Circumference = 2πr = dπ
0°180°
90°
270°
135°
315°
Pie Charts Probability0 = no chance1 = for sure
135º ------ = 3/8360º or .375 or 37.5%
180º ------ = 1/2360º or .5 or 50%
45º ------ = 1/8360º or .125 or 12.5%
ALGEBRA: Given Diameter RT
Find .
Substitution
Simplify.
Add 2 to each side.
Divide each side by 26.
Use the value of x to findGiven
Substitution
Answer: 52
The sum of the measures of
ALGEBRA Refer to .
Find .
Linear pairs are supplementary.
Substitution
Simplify.
Subtract 140 from each side.
form a linear pair.
Answer: 40
Answer: 65
Answer: 40
ALGEBRA AD and BE are diameters
a. Find m
b. Find m
Find .
In bisects and
is a minor arc, so
is a semicircle.
Answer: 90
Find .
In bisects and
since bisects .
is a semicircle.
Answer: 67
Find .
In bisects and
Answer: 316
Answer: 54
Answer: 72
In and are diameters, and bisects Find each measure.
a.
b.
c.
Answer: 234
In and .
a) Find the length of .
b) Find the length of arc DC.
In and . Write a proportion to compare each part to its whole.
degree measure of arcdegree measure of
whole circle
arc lengthcircumference
Example 2-4b
Now solve the proportion for .
Simplify.
Answer: The length of is units or about 3.14 units.
Multiply each side by 9 .
Answer: The length of arc DC is 7π/2 units or about 11 units.
C ∙ (% of the circle) = 9π ∙ (140/360)
= 7π/2
Summary & Homework
• Summary:– Sum of measures of central angles of a circle with
no interior points in common is 360°– Measure of each arc is related to the measure of
its central angle– Length of an arc is proportional to the length of
the circumference
• Homework: – pg 533-534; 14-19; 24-29; 32-35