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Warm-Up
Geometry
Inscribed Angles and Other Relationships
Vocabulary

Central Angle – an angle whose vertex is
on the center of a circle. The arc
measure is equal to the measure of the
central angle.

Inscribed Angle – an angle whose vertex
is on a circle.

Intercepted Arc – the arc that lies
between an inscribed angle.
Investigation Activity
Use trace paper to create angles RTS,
RUS, and RVS.
 Compare the four angles to each other
(RPS, RTS, RUS, RVS). What do you
notice?

Theorems

Draw a right triangle in your circle. How
do you know it is a right triangle?

Draw a quadrilateral in your circle. What
can you conclude about the angles of
your quadrilateral?
Theorems
Practice
1
m∠BAC = 2 𝐵𝐶
1
1
m∠BAC = 2 𝐵𝐶
1
m∠BAC = 2 160°
78° = 2 𝐵𝐶
m∠BAC =80°
2 ∙ 78° = 2 𝐵𝐶 ∙ 2
1
156° = 𝐵𝐶
Practice
2x + 100° = 180° y + 87° = 180°
-100° -100°
-87° -87°
2x
x
= 80°
= 40
y
2y + 5x = 180°
3y + 3x = 180°
2(60°-x) +5x = 180°
y + x = 60°
120° -2x +5x = 180°
y = 60° - x
3x = 60°
y =60° - 20°
x = 20°
y =40°
= 93°
10.4 – Other Relationships in
Circles.
Practice

Since the intersection occurs inside of the
circle. We add the two intercepted arcs
formed by the angle and its vertical angle.
Practice

Since the intersection occurs outside of
the circle. We subtract the arcs formed by
the angle and then divide by two.
Practice

Since the intersection occurs outside of
the circle. We subtract the arcs formed by
the angle and then divide by two.
Practice
Practice
Exit Ticket

Copy down one
of the pictures
and examples that
we completed in
class and turn it
in.
Homework
Pg. 617: 9-23 odd
 Pg. 624: 9-27 odd
