9-4
Inscribed Angles
Objectives:
• To recognize and find measures of inscribed angles.
• To find properties of inscribed angles.
Vocabulary
• Inscribed Angle
• Intercepted Arc
Inscribed Angle
• An inscribed angle is an
angle whose vertex is on
the circle and whose
sides contain chords of
the circle.
Intercepted Arc
• In this circle we would
say that angle FAB
intercepts arc FDB. Arc
FDB is called the
intercepted arc.
Theorem 9-4
• If an angle is inscribed in a circle, then the
measure of the angle equals one-half the
measure of its intercepted arc.
Example 1
Theorem 9-5
• If two inscribed angles of a
circle or congruent circles
intercept congruent arcs or
the same arc, then the
angles are congruent.
Theorem 9-6
• If an inscribed angle of a
circle intercepts a
semicircle then the angle is
a right angle.
Theorem 9-7
• If a quadrilateral is
inscribed in a circle, then
its opposite angles are
supplementary