Parallel And Perpendicular Lines Worksheet Page 30
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50Angle relationships can be used to solve problems involving unknown values.
Solve Problems with Parallel Lines
Example
Example
2
2
m
ALGEBRA
m n
Find x and m RSU so that
.
U
( 8 x
4 )
˚
R
n
V
Explore
From the figure, you know that
( 9 x
11 )
˚
S
m RSU
8x
4 and m STV
T
RSU
9x
11. You also know that
and
STV are corresponding angles.
Plan
m
n
For line
to be parallel to line
, the corresponding angles must be
congruent. So, m RSU
m STV. Substitute the given angle measures
into this equation and solve for x. Once you know the value of x, use
substitution to find m RSU.
Solve
m RSU
m STV
Corresponding angles
8x
4
9x
11
Substitution
x
4
11
Subtract 8x from each side.
15
x
Add 11 to each side.
Now use the value of x to find m RSU.
m RSU
8x
4
Original equation
8(15)
4
x
15
124
Simplify.
Examine Verify the angle measure by using the value of x to find m STV.
That is, 9x
11
9(15)
11 or 124. Since m RSU
m STV,
m n
RSU
STV and
.
PROVE LINES PARALLEL
The angle pair relationships formed by a
transversal can be used to prove that two lines are parallel.
Study Tip
Prove Lines Parallel
Example
Example
3
3
Proving Lines
Parallel
Given:
r s
s
When proving lines
5
6
m
4
parallel, be sure to
6
r
5
check for congruent
Prove:
m
7
corresponding angles,
alternate interior angles,
alternate exterior angles,
Proof:
or supplementary
consecutive interior
Statements
Reasons
angles.
r s
1.
,
5
6
1. Given
2.
4 and
5 are supplementary.
2. Consecutive Interior Angle Theorem
3. m 4
m 5
180
3. Definition of supplementary angles
4. m 5
m 6
4. Definition of congruent angles
5. m 4
m 6
180
5. Substitution Property ( )
6.
4 and
6 are supplementary.
6. Definition of supplementary angles
m
7.
7. If cons. int.
are suppl., then lines
are .
Lesson 3-5 Proving Lines Parallel 153
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