geometry geometry geometrygeometry 9.3 arcs and central angles
TRANSCRIPT
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Geo
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Angles
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Objectives
• At the completion of the lesson, you will be able to…
• Define and identify arcs and central angles in circles
• Calculate the measures of arcs and central angles in circles
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Using Arcs of Circles
Central Angle – an angle whose vertex is at the center of a circle
Major Arc – formed by two points on a circle and its measure is greater than 180; named with 3 endpoints
Minor Arc – formed by two points on a circle whose measure is less than 180; named with 2 endpoints
central angle
minorarcmajor
arcP
B
A
C
Semicircle – an arc formed by two points on a circle whose measure is equal to 180
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Example: Naming Arcs
• Name:– minor arcs:
– major arcs:
– semicircles:
– An acute central angle:
– Two congruent arcs:
EH F
G
E
60°
60°
180°
•B
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Measuring arcs
Measure of an arc: equal to the measure of an arc’s central angleMinor arc:
Major arc – think about it: how would I find
EH F
G
E
60°
60°
180°
•B
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A postulate
Arc Addition Postulate
• The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs.
B
A
C
m = m + m ABC
AB
BC
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Ex. 1: Finding Measures of Arcs
• Find the measure of each arc of R.
a. b. c.
MNMPNPMN
PR
M
N80°
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Ex. 2: Finding Measures of Arcs
• Find the measure of each arc.
a. b. c.
GE
GEFR
EF
G
H
GF
40°
80°
110°
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Congruent arcs
• Arcs, in the same circle or in congruent circles, that have equal measures
C
D
A
BAB• and are in
the same circle and
m = m = 45°. So,
DC
ABDCDC
AB
45°
45°
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Homework
• Page 341 Classroom exercises 1-13
• Page 341 Written Exercises 1-8• Quiz tomorrow on 9.1-9.3