Parallel and Perpendicular Lines Unit
Day 1
Name_________________________
Use the Law of Detachment to make a valid conclusion.
1. If the measure of an angle is less than 90°, then the angle is acute.
The measure of  A is 46°.
2. Find the measure of each numbered angle.
3. Find the value of x and the measure of
each angle.
120
1
3
2
(5x + 17)
Identifying Pairs of Lines and Angles
Parallel lines –
Skew lines –
Parallel planes –
(3x + 27)
Example 1
Think of each segment in the figure as part of line.
Which line(s) or plane(s) in the figure appear to fit
the description?
C
B
a. Line(s) parallel to CD and containing point A.
D
A
b. Line(s) skew to CD and containing point A.
c. Line(s) perpendicular to CD and containing point A.
F
E
G
H
d. Plane(s) parallel to plane EFG and containing point A.
Parallel Postulate – If there is a line and a point not on the line, then there is exactly one line
through the point parallel to the given line.
Perpendicular Postulate – If there is a line and a point not on the line, then there is exactly one line
through the point perpendicular to the given line.
Transversal –
Angles Formed by Transversals
corresponding angles
alternate interior angles
t
t
alternate exterior angles
consecutive interior angles
t
t
Example 2
Identify all pairs of angles of the given type.
a. corresponding
b. alternate interior
1 2
3 4
c. alternate exterior
5 6
7 8
d. consecutive interior
Example 3
Classify the pair of numbered angles.
a.
b.
c.
2
1
5
5
7
4
Finding and Using Slopes of Lines
slope –
m
rise change in y y 2  y1


run change in x x 2  x1
Slopes of Lines in the Coordinate Plane:
negative slope –
positive slope –
zero slope (slope of 0) –
undefined slope (no slope) –
Example 1
Find the slope of each line given a set of endpoints.
a. (4, 6), (3, 8)
b. (2, – 1), (2, 9)
c. (–6, 5), (–2, 3)
Parallel lines –
m1 = m2
Perpendicular lines –
m1  m2= -1
d. (1, 7), (10, 7)
Example 2
Find the slope of each line. Which lines are parallel?
a
b
c
Example 3
Line h passes through (3, 0) and (7, 6). Graph the line perpendicular to h that passes through the
point (2, 5).
Example 4
Line m passes through (–1, 3) and (4, 1). Line t passes through (–2, –1) and (3, –3). Are the two
lines parallel? Explain how you know.
Example 5
Tell whether the lines through the given points are parallel, perpendicular, or neither. Show work
to justify your answer!!
a.
Line 1: (1, 0), (7, 4)
b.
Line 1: (–3, 1), (–7, –2)
Line 2: (7, 0), (3, 6)
Line 2: (2, –1), (8, 4)