Angles Geometry ObjectivesAssignment Use inscribed angles to solve problems Use properties of inscribed polygons Review Definitions An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle ID: 485649
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Slide1
9.4 Inscribed Angles
GeometrySlide2Slide3
Objectives/Assignment
Use
inscribed angles to solve problems.
Use properties of inscribed polygons
.Slide4
ReviewSlide5
Definitions
An
inscribed angle
is an angle whose vertex is on a circle and whose sides contain chords of the circle.
The
arc that lies in the interior of an inscribed angle and has endpoints on the angle is called the
intercepted arc
of the angle.Slide6
Theorem 9.4: Measure of an Inscribed Angle
m ADB
= ½mSlide7
Finding Measures of Arcs and Inscribed Angles
Find the measure of the blue arc or angle.
m = 2m
QRS =
2(90
°
) = 180
°Slide8
Finding Measures of Arcs and Inscribed Angles
Find the measure of the blue arc or
angle if
ZYX = 115
°.
m = 2m
ZYX
2(115
°
) = 230
°Slide9
Finding Measures of Arcs and Inscribed Angles
Find the measure of the blue arc or angle.
m = ½ m
½ (100
°
) = 50
°
100
°Slide10
Theorem 9.5
C DSlide11
Comparing Measures of Inscribed Angles
Find
m
ACB
,
m
ADB
, and
m
AEB
if AB = 60 °.
The measure of each angle is half the measure of m = 60
°, so the measure of each angle is 30°Slide12
Finding the Measure of an Angle
Given m
E
= 75
°. What is m
F
?
E and F both intercept , so E F. So,
mF
=
mE
= 75°
75
°Slide13
Find x
.
AB is a diameter. So,
C is a right angle and
mC
= 90
°
2x° = 90°
x = 45
2x
°Slide14
½ *
96 = (2x + 1)
48 = 2x + 1
47 = 2x
X = 23.5
m
PQR =
½
m PRSlide15
x = 2x – 3
- x = -3
X = 3Slide16
m
P = 90
½ x + (1/3 x +5) = 90
5/6 x +
5 = 90
5/6
x = 85
X
= 102Slide17
PracticeSlide18