Parallel And Perpendicular Lines Worksheet Page 46
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50Chapter 3 Study Guide and Review
Chapter 3 Study Guide and Review
Exercises
Determine whether AB and CD are parallel, perpendicular, or neither.
See Example 3 on page 141.
23. A( 4, 1), B(3,
1), C(2, 2), D(0, 9)
24. A(6, 2), B(2,
2), C( 1,
4), D(5, 2)
25. A(1,
3), B(4, 5), C(1,
1), D( 7, 2)
26. A(2, 0), B(6, 3), C( 1,
4), D(3,
1)
Graph the line that satisfies each condition.
See Example 4 on page 141.
27. contains (2, 3) and is parallel to AB with A( 1, 2) and B(1, 6)
28. contains ( 2,
2) and is perpendicular to PQ with P(5, 2) and Q(3,
4)
3-4
3-4
Equations of Lines
See pages
Concept Summary
145–150.
In general, an equation of a line can be written if you are given:
•
slope and the y-intercept
•
the slope and the coordinates of a point on the line, or
•
the coordinates of two points on the line.
Example
Example
Write an equation in slope-intercept form of the line that passes through (2,
4)
and ( 3, 1).
Find the slope of the line.
Now use the point-slope form and
either point to write an equation.
y
y
2
1
m
y
y
m(x
x
)
Slope Formula
Point-slope form
1
1
x
x
2
1
y
( 4)
1(x
2)
m
1, (x
, y
)
(2,
4)
1
( 4
)
(x
, y
)
(2,
4),
1
1
1
1
(x
, y
)
( 3, 1)
3
2
y
4
x
2
2
2
Simplify.
5
or
1
Simplify.
y
x
2
Subtract 4 from each side.
5
Exercises
Write an equation in slope-intercept form of the line that satisfies the
given conditions.
See Examples 1–3 on pages 145 and 146.
29. m
2, contains (1,
5)
30. contains (2, 5) and ( 2,
1)
2
3
31. m
, y-intercept
4
32. m
, contains (2,
4)
7
2
33. m
5, y-intercept
3
34. contains (3,
1) and ( 4, 6)
3-5
Proving Lines Parallel
3-5
See pages
Concept Summary
151–157.
When lines are cut by a transversal, certain angle relationships produce parallel lines.
•
congruent corresponding angles
•
congruent alternate interior angles
•
congruent alternate exterior angles
•
supplementary consecutive interior angles
Chapter 3 Study Guide and Review 169
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