Parallel Lines & Transversals
P. 307 – 308
Objectives
Identify parallel lines and the angles
formed by parallel lines and
transversals
Transversal
A transversal is a line, ray, or segment
that intersects two or more lines, rays,
or segments, each at a different point
Notice – according to the definition, the
lines, rays, or segments that are cut by
the transversal do not have to be
parallel
Special Angle Relationships:
Names that describe where the angles are located
INTERIOR means
BETWEEN the parallel
lines
EXTERIOR means
OUTSIDE the parallel lines
ALTERNATE means
OPPOSITE sides of the
transversal
Alternate Interior Angles
Measures are equal
These angles are
“friendly” because
their name clearly
describes “where”
they are located
Corresponding Angles
Measures are equal
Location (the name doesn’t
tell you)
On the same side of the
transversal
One interior and one
exterior
They are NOT adjacent
They lie on the same
side of the transversal
Vertical Angles
Two angles formed by intersecting lines
They are across from one another in
the corners of the “X” and they are
always equal
Adjacent Angles
Creating a Straight Line
Two angles which share a vertex, a
common side, but do not overlap
(share no interior points)
Measures are supplementary
Example
Describe the relationship between the
angles
Example - Solution
Describe the relationship between the
angles
Alternate Interior angles
Example
List all pairs of angles that fit the
description
a. corresponding
b. alternate interior
Example - Solution
List all pairs of angles that fit the
description
a. corresponding
<1 and <5, <2 and <6,
<3 and <7, <4 and <8
b. alternate interior
<2 and <7, <4 and <5
Summary
When a transversal intersects two
parallel lines:
Alternate interior angles are congruent
Corresponding angles are congruent
Check Point
Describe the relationship between the
angles
1. <1 and <5
2. <4 and <5
3. <4 and <8
Check Point - Solutions
Describe the relationship between the
angles
1. <1 and <5
Corresponding
2. <4 and <5
Alternate Interior
3. <4 and <8
Corresponding
Practice
Using the diagram below in which l || m,
suppose that m<1 = 34°. What are the
measures of the other angles in the
diagram.
Practice - Solution
Using the diagram below in which l || m,
suppose that m<1 = 34°. What are the
measures of the other angles in the
diagram.
<2, <5, <8 = 34 degrees
<3, <4, <6, <7 = 146 degrees
Practice
Given: r || s and m<1 = 60 degrees
Find: the measures of the other seven
angles
Practice - Solution
Given: r || s and m<1 = 60 degrees
Find: the measures of the other seven
angles
<2, <4, <6, <8 = 120
<3, <5, <7 = 60