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Section 10.4 Notes: Inscribed
Angles
Learning Targets
Students will be able to find measures of inscribed
angles.
Students will be able to find measures of angles of
inscribed polygons.
Vocabulary!
has a vertex on a circle and sides that contain
Inscribed Angle chords of the circle.
has endpoints on the sides of an inscribed
angle and lies in the interior of the inscribed
Intercepted Arc angle
∠𝑄𝑅𝑆 𝑖𝑠 𝑎𝑛 𝒊𝒏𝒔𝒄𝒓𝒊𝒃𝒆𝒅 𝒂𝒏𝒈𝒍𝒆
𝑄𝑆 𝑖𝑠 𝑡ℎ𝑒 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕𝒆𝒅 𝒂𝒓𝒄
Vocabulary!
If an angle is inscribed in a circle, then the
measure of the angle equals one half the
measure of its intercepted arc
Inscribed Angle
Theorem
𝐴𝐵
2
2 𝑚∠1 = 𝐴𝐵
𝑚∠1 =
Example 1:
a) Find 𝑚∠𝑋.
Example 1:
b) Find m𝑌𝑋
Example 1:
c) Find 𝑚∠𝐶.
Example 1:
d) Find 𝑚𝐵𝐶.
Vocabulary!
Theorem 10.7
If two inscribed angles of a circle intercept
the same arc or congruent arcs, then the
angles are congruent.
Example 2:
a) Find measure of 𝑚∠𝑅.
Example 2:
b) Find 𝑚∠𝐼.
Vocabulary!
An inscribed angle of a triangle intercepts a
diameter or semicircle if and only if the angle
is a right angle.
Theorem 10.8
Example 3:
a) Find 𝑚∠ 𝐵.
Example 3:
b) Find 𝑚∠ 𝐷.
Add to your notes!
Theorem 10.9
If a quadrilateral is inscribed in a circle, then its
opposite angles are supplementary.
Example 4:
a) An insignia is an emblem that signifies rank,
achievement, membership, and so on. The
insignia shown is a quadrilateral inscribed in a
circle. Find angle S and angle T.
Example 4:
b) An insignia is an emblem that signifies rank,
achievement, membership, and so on. The
insignia shown is a quadrilateral inscribed in a
circle. Find measure of angle N.
Summary!
Summary! Writing in math
A 45-45-90 right triangle is inscribed in a circle.
If the radius of the circle is given, explain how
to find the lengths of the right triangle’s legs.