Download 10.4 Practice with Examples

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Problem of Apollonius wikipedia, lookup

Rational trigonometry wikipedia, lookup

3-manifold wikipedia, lookup

Four color theorem wikipedia, lookup

Trigonometric functions wikipedia, lookup

Riemann–Roch theorem wikipedia, lookup

Line (geometry) wikipedia, lookup

Noether's theorem wikipedia, lookup

Geometrization conjecture wikipedia, lookup

Brouwer fixed-point theorem wikipedia, lookup

Pythagorean theorem wikipedia, lookup

History of geometry wikipedia, lookup

History of trigonometry wikipedia, lookup

Euclidean geometry wikipedia, lookup

Transcript
Chapter 10
LESSON
10.4
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 621–627
GOAL
Use angles formed by tangents and chords to solve problems in
geometry and use angles formed by lines that intersect a circle to
solve problems
VOCABULARY
Theorem 10.12
If a tangent and a chord intersect at a point on a circle, then the measure
of each angle formed is one half the measure of its intercepted arc.
Theorem 10.13
If two chords intersect in the interior of a circle, then the measure of
each angle is one half the sum of the measures of the arcs intercepted by
the angle and its vertical angle.
Theorem 10.14
If a tangent and a secant, two tangents, or two secants intersect in the
exterior of a circle, then the measure of the angle formed is one half the
difference of the measures of the intercepted arcs.
EXAMPLE 1
Finding Angle and Arc Measures
Line m is tangent to the circle.
a. Find m1
b. mACB
90
B
A
1
2
m
SOLUTION
1
2
C
a. m1 90 45
b. Because 1 and 2 are a linear pair,
m2 180 m1 180 45 135. So,
mACB 2135 270.
190
Geometry
Practice Workbook with Examples
Copyright © McDougal Littell Inc.
All rights reserved.
LESSON
Practice with Examples
Chapter 10
10.4
CONTINUED
NAME _________________________________________________________ DATE ____________
For use with pages 621–627
Exercises for Example 1
Find the value of each variable.
1.
2.
B
3.
M
m
P
x
156
z
2x
C
1
EXAMPLE 2
x
2
x
y A
Q
m
m
y
N
Using Theorem 10.13
Find the value of x.
SOLUTION
A
1 x mAB
mCD
2
Apply Theorem 10.13. 60
B
1
x 60 20 Substitute.
2
x 40
x
D
20
C
Simplify.
Exercises for Example 2
Find the value of x.
4.
5.
A
N
135
M
6.
30
P
W
x
2x
45
B
C
x
D
Copyright © McDougal Littell Inc.
All rights reserved.
110
100
Y
x
Z
X
Q
Geometry
Practice Workbook with Examples
191
Chapter 10
LESSON
10.4
CONTINUED
EXAMPLE 3
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 621–627
Using Theorem 10.14
Find the value of x.
A
D
B
x
SOLUTION
85
E
1
x mBC mDE
2
Apply Theorem 10.14.
1
x 171 85
2
Substitute.
x 43
171
C
Simplify.
Exercises for Example 3
Find the value of x.
7.
8.
x
9.
30
136
60
38 x 2x
8x
170
192
Geometry
Practice Workbook with Examples
Copyright © McDougal Littell Inc.
All rights reserved.