Download Geometry 11-4

Warm-Up
• Find the area of the shaded region.
10m
140°
Geometry 11-4
Inscribed Angles
Vocabulary
• Inscribed angle- an angle whose vertex is
on the circle and whose sides are chords.
Vocabulary
• Intercepted arc- the arc created by an
inscribed angle (between the chords)
Theorem 1
• The measure of an inscribed angle is half the
measure of its intercepted arc.
A
100°
C
50°
B
1
mABC  AC
2
Example
• Find each measure.
mPRU
PS
Example
• Find the value of a.
Theorem 2
• If two inscribed angles have the same
intercepted arc, then the two inscribed
angles are congruent.
C
mABC  mADC
D
A
B
Theorem 3
• If a quadrilateral is inscribed in a circle, then
its opposite angles are supplementary.
D
C
A  C  180
B  D  180
A
B
Example
• Find each angle measure.