Download Geo_Lesson 10_3

Bellwork 10.3 Name: _____________________
mAC = _______

mADG = _______

x = ______

CF = _______ DF = _______
2x – 4

6x – 24
Find the indicated value:
 Show calculations to get credit

Geometry Lesson 10.3
Inscribed Angles
May 6, 2008
1. Inscribed Angles & Arcs
angle:
Vertex is on the
circle and sides
contain chords
 Intercepted arc:
The arc on the
interior of an
inscribed angle
A
 Inscribed
B
C
ABC is inscribed
AC is intercepted
by ABC
Measure of an Inscribed Angle
10.8: IF an
angle is inscribed
in a circle,
B
THEN its measure is
half the measure of
the intercepted arc
A
 Thm
P
mABC = 1/2 mAC
C
Using Measures of Inscribed Angles

Find the measure of the indicated arc or angle
1.
2.
mBC =
2(38°) = 76°
4.
mBC =
74°
3.
mBC =
5.
2 (78°)= 156°
mBAC =
½ (160°) =80°
mBAC =
½ (87°)=43.5°
2. Same Intercepted Arc Theorem
10.8: IF two
inscribed angles
intercept the
same arc,
THEN they are
congruent
A
 Thm
B
D
ABC  ADC
C
Using Same Inscribed Angles
Find the value of x
6.
7.

x° = 50°
(intercept
same arc)
(3x+5)° = 80°
3x° = 75°
x = 25
(intercept
same arc)
8.
3. Inscribed Polygons
polygon:
All vertices lie on a
circle
B
 Circumscribed
circle: A circle with
an inscribed
C
polygon
A
 Inscribed
E
P
D
Pentagon ABCDE is inscribed in P
P is circumscribed about ABCDE
Inscribed Polygon Theorems
Thm 10.10: If a right
triangle in inscribed,
then its hypotenuse is
a diameter
 Thm 10.11: A
quadrilateral can be
inscribed IFF its
opposite angles are
supplementary

A
AC is
diam.
P
C
B
E
H
P
F
EFGH are on P IFF mE + mG = 180°
and mF + mH = 180°
G
Using Inscribed Polygon Theorems
Find the value of each variable
9.
10.

4x°
11.
5x°
4x + 5x = 90°
9x=90°
X = 10
12.
X + 90 = 180
X = 90
X = 10
X +105° = 180
X = 75°
13.
2y + y = 180
3y = 180
Y = 60
14.
X = 90
Y = 93°
Independent Practice
Ch 10.3 (pp. 616-617)
3-23 all