Page 166 - Math Course 3 (Book 2)

Inscribed Angles
Mo. 11

Lesson 4
THEOREM 11.6

If two inscribed angles of a circle (or congruent
KEY CONCEPTS:
circles) intercept congruent arc or the same arc,
1. Find measures of inscribed angles. then the angles are congruent.
2. Find measures of angles of inscribed
polygons. Abbreviations:
Inscribed ⦞ of arcs are ≅.

Inscribed ⦞ of same arc are ≅.
MO. 11 - L4a
A B B
A C
Measures of Inscribed Angles
F
D

Vocabulary A-Z D C E

Let us learn some vocabulary ∠DAC ≅ ∠DBC ∠FAE ≅ ∠CBD

intercepted
Corresponding to an angle, this is the arc of a circle Let’s Begin
that lies in the interior of the angle together with the
endpoints of the arc.

ADC is the arc intercepted by ∠ABC. Measures of Inscribed Angles

Example
B
A
In ⊙F, mWX = 20, mXY = 40, mUZ = 108, and
mUW = mYZ. Find the measures of the numbered
intercepted angles.
D

C W X

THEOREM 11.5 3 Y

Inscribed Angle Theorem 4 5
2
If an angle is inscribed in a circle, F
then the measure of the angle
equals one-half the measure if its B U
intercepted arc(or the measure A
of the intercepted arc is twice the
measure of the inscribed angle). 1
1 D C Z
Example: m∠ABC = (mADC) or T
2

2(m∠ABC) = mADC

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