Transcript Lesson 1 Contents

Transparency 10-4
5-Minute Check on Lesson 10-3
The radius of ⊙R is 35, LM  NO, LM = 45 and mLM = 80.
Find each measure.
1. m NO
80°
2. m NQ
40°
3. NO
45
4. NT
22.5
5. RT
26.81
6.
Which congruence statement is true if RS
and TU are congruent chords of ⊙V?
Standardized Test Practice:
A
RS  SU
B
RS  TU
C
ST  RU
Click the mouse button or press the
Space Bar to display the answers.
D
RS  ST
Lesson 10-4
Inscribed Angles
Objectives
• Find measures of inscribed angles
• Find measures of angles of inscribed polygons
Vocabulary
• Inscribed Angle – an angle with its vertex on
the circle and chords as its sides
Circles – Inscribed Angles
y
J
Y°
x
Center
F
X°
E
K
Measure Y° = ½ measure Arc KEF
In
and
Find the measures of the numbered angles.
First determine
Arc Addition Theorem
Simplify.
Subtract 168 from each side.
Divide each side by 2.
So,
m
Answer:
In
and
measures of the numbered angles.
Answer:
Find the
ALGEBRA Triangles TVU and TSU are inscribed in
with
Find the measure of each
numbered angle if
and
∆UVT and ∆ UST are right
triangles. Since they intercept
congruent arcs, then m1 =
m2. The third angles of the
triangles must also be
congruent, so m2 = m4 .
Angle Sum Theorem
Simplify.
Subtract 105 from each side.
Divide each side by 3.
Use the value of x to find the measures of
Given
Given
Answer:
ALGEBRA Triangles MNO and MPO are inscribed
in
with
Find the measure of each
numbered angle if
and
Answer:
Quadrilateral QRST is inscribed in
Find
and
Draw a sketch of this situation.
If
and
To find
To find
we need to know
first find
Inscribed Angle Theorem
Sum of angles in circle = 360
Subtract 174 from each side.
Inscribed Angle Theorem
Substitution
Divide each side by 2.
To find
find
we need to know
but first we must
Inscribed Angle Theorem
Sum of angles in circle = 360
Subtract 204 from each side.
Inscribed Angle Theorem
Divide each side by 2.
Answer:
Quadrilateral BCDE is inscribed in
find
and
Answer:
If
and
Summary & Homework
• Summary:
– The measure of the inscribed angle is half the
measure of its intercepted arc
– The angles of inscribed polygons can be found by
using arc measures
• Homework:
– pg 549-550; 7, 9,10, 15, 22-25