Download 14.2 The Inscribed Angle Theorem

Geometry 14.2: Chord Length and Arc Measures
14.2 The Inscribed Angle Theorem
Background vocabulary:
Ø
Radius
Ø
Diameter
Ø
Arc (major and minor)
Ø
Central Angle
Ø
Chord
Definition:
Inscribed Angle
An angle whose vertex is on the circle and each side of the angle intersects the circle at two(2) distinct points.
B
A
C
Inscribed Angle Theorem:
m = 1/2 m arc it intersects
B
700
350
C
A
Semi­Circle Theorem:
An angle inscribed in a semi­circle
is a right angle.
Same­Arc Theorem:
In a circle, if two inscribed angles intercept the same arc, then the two(2) angles are congruent.
Whats true about ≮A & ≮B?
A
D
B
C
1.
2.
U
V
1120
1
340
m arcUV=
m≮1=
3.
3
1120
m≮3=
4.
920
580
1000
E
m arcEF=
F
Q
5.
P
Find the m≮R:
2n0
180­3n0
Justify your answer!
n0
T
S
R
6. The three angles of
have measures 40, 60, and 80. If
the circle through ABC is drawn, what are the measures of the
three minor arcs formed by the points.
7. ABCDEF is a regular hexagon. Find m≮BFE:
7.
A
B
F
C
E
D
Find m≮BFE=
Review:
A
1. Name the central angle?_________________
Radius
2. Segment BC is a ?______________________
Central
minor arc.
angle is = to the degree of its ___________
3. The degree measure of the ______________
C
B
Congruent Circles:
radii
4. Two circles are congruent when their ______________
are congruent.
5. Theorem: If two arcs have the same measure, they
are congruent and their chords are congruent.
6. Theorem: If two chords have the same length, their
minor arcs have the same measure.
7. Draw a picture of both of these theorems and label
pieces that make these true.
4. Theorem: If two arcs have the same measure, they
are congruent and their chords are congruent.
5. Theorem: If two chords have the same length, their
minor arcs have the same measure.
6. Draw a picture of both of these theorems and label
pieces that make these true.
Are the measures of arcs AB congruent below
for the two circles below? Why/why not?
8.
A
A
8
4
c 60 B
o
c
60o
B
Label a major and minor arc.
9.
A
B
4
D
C
12
AD=
BC=
AB=