Transcript Inscribed Angles

Inscribed Angles
Inscribed Angles – An angle
that has its vertex on the
circle and its sides
contained in chords of the
circle.
Intercepted – An angle intercepts
an arc if and only if the
following conditions are met:
1. The endpoints of the arc lie on
the angle.
2. All points of the arc except the
endpoints are in the interior of
the angle.
3. Each side of the angle contains
an endpoint of the arc.
D
C
A
B
Inscribed Angles
Inscribed Angle Theorem
• An inscribed angle is
equal in measure to half
its intercepted arc.
Theorem 10.6
• Inscribed angles that
intercept the same arc or
congruent arcs are equal.
Theorem 10.7
• An inscribed angle that
intercepts a semicircle is a
right angle.
D
C
A
E
B
Inscribed Angles
B
Theorem 10.8
• If a quadrilateral is
inscribed in a circle,
then its opposite
angles are
supplementary.
A
D
C
E
In
and
measures of the numbered angles.
Answer:
Find the
ALGEBRA Triangles MNO and MPO are inscribed
in
with
Find the measure of each
numbered angle if
and
Answer:
Quadrilateral BCDE is inscribed in
find
and
Answer:
If
and