February 09, 2017
(10.3)Pg.719: 7-15odd, 16-20, 24, 26, 27, 31, 35
Even Solutions
16. 11
18. 42o
20. 57.6o
Y
February 09, 2017
February 09, 2017
26.
February 09, 2017
February 09, 2017
(10.4 - Good Buddy) Inscribed Angles
Objective: To find the measures of inscribed angles and angles
of inscribed polygons
Why: To understand the relationships that exist within circles.
Also, many designs and logos use the principles of inscribed
angles as well as reflection principles in science.
Ex.
The diagram shows how light bends in a rain drop to form the
colors of the rainbow.
Ex. A STOP sign.
STOP
February 09, 2017
Obj: To find the measures of inscribed angles and angles of
inscribed polygons
Defn.
Inscribed Angle:
C
B
A
intercepted arc:
Inscribed Angle Theorem: The measure of an inscribed angle is half
the measure of its intercepted arc.
Proof:
Statement
Reason
February 09, 2017
Obj: To find the measures of inscribed angles and angles of
inscribed polygons
What can you conclude about
A
B and
D?
C
B
D
Theorem: If two inscribed angles intercept the same arc or
congruent arcs, then they are congruent.
February 09, 2017
Obj: To find the measures of inscribed angles and angles of
inscribed polygons
February 09, 2017
Obj: To find the measures of inscribed angles and angles of
inscribed polygons
February 09, 2017
Obj: To find the measures of inscribed angles and angles of
inscribed polygons
Statements
Reasons
February 09, 2017
Obj: To find the measures of inscribed angles and angles of
inscribed polygons
B
A
P
C
Theorem: An inscribed angle of a triangle intercepts a diameter
IFF it is a right angle.
February 09, 2017
Obj: To find the measures of inscribed angles and angles of
inscribed polygons
February 09, 2017
Obj: To find the measures of inscribed angles and angles of
inscribed polygons
B
A
C
D
Theorem: If a quadrilateral is inscribed in a circle, then its
opposite angles are supplementary.
February 09, 2017
Obj: To find the measures of inscribed angles and angles of
inscribed polygons
The necklace charm uses a quadrilateral
inscribed a circle. Find the m A and m
B.
February 09, 2017
Obj: To find the measures of inscribed angles and angles of
inscribed polygons
Inscribed Angle Theorem: The measure of an inscribed angle is half
the measure of its intercepted arc.
Theorem: If two inscribed angles intercept the same arc or
congruent arcs, then they are congruent.
Theorem: An inscribed angle of a triangle intercepts a diameter
IFF it is a right angle.
Theorem: If a quadrilateral is inscribed in a circle, then its
opposite angles are supplementary.
February 09, 2017
Obj: To find the measures of inscribed angles and angles of
inscribed polygons
HW:
(HR): (10.4) Pg. 727: 11, 13, 15, 17-20, 22-24, 27, 28
February 09, 2017
Obj: To find the measures of inscribed angles and angles of
inscribed polygons
EXIT SLIP:
Find the m
A.
A
STOP