 Color one pair of
alternate exterior angles
purple and the other
orange.
 Color one pair of
alternate interior angles
red and the other
yellow.

Sign for parallel: m || n
In the diagram on the right, parallel lines m and
n have been “cut” (intersected) by a transversal,
t. When two parallel lines are cut by a
transversal, certain angle relationships are
formed.
Parallel Lines and Transversals
Color one pair of
vertical angles blue
and the other green.
 Exterior angles that lie
on __________ sides of
the transversal and on
________ parallel lines.
 If the lines are parallel,
then they are ________.
 The angles that are
alternate exterior in the
figure below are:
 Interior angles that lie
on __________ sides of
the transversal and on
________ parallel lines.
 If the lines are parallel,
then they are ________.
 The angles that are
alternate interior in the
figure below are:
 Congruent angles
formed by two
intersecting lines.
 The angles that are
vertical in the
figure below are:
Alternate Alternate
Vertical
Interior Exterior
Angles Angles
Angles
 Color each pair of
corresponding angles a
different color.
 Angles that lie on the
________ side of the
transversal and in
___________ positions.
 The angles that are
corresponding in the
figure below are:
Parallel Lines and Transversals – Guided Practice
Example 1: Use the diagram to answer the following questions. A || B
and T is a transversal.

Are angles 1 and 3 congruent?
How do you know?

Are angles 4 and 6 congruent? How do you know?

If angle 2 is 145°, determine the measurements of all the angles.
Justify your answers using angle relationships.
-----------------------------------------------------------------------------------------Example 2: Given: p || q and w is a transversal.

Which angles are congruent?
Explain.

If angle 2 is 132°, what is the measure of angle 7? Justify your
answer.
Example 3: Use the diagram to find the measures of the angles. List
the reason below
a.) mÐa = _______ Reason? ___________
b.) mÐb = _______ Reason? ___________
Example 5: Lines m and n are parallel, and line t is a transversal.
a.) Use the diagram to find x.
What relationship did you use
set up your equation?
c.) mÐc = _______ Reason? ___________
d.) mÐd = _______ Reason? ___________
e.) mÐe = _______ Reason? ___________
Is there a different way to find e?
b.) Determine the measures for all the angles.
________________________________________________________
f.) mÐf = _______ Reason? ___________
Is there a different way to find f?
________________________________________________________
------------------------------------------------------------------------------------------
-----------------------------------------------------------------------------------------Example 6: In the diagram lines j and k are parallel.
a.) What is the value of x?
How do you know?
Example 4: Line p and q are parallel. Give three ways to reason that
angle 1 and angle 7 are congruent.
Reason 1: _______________________
b.) What is the value of y? How do you know?
________________________________
________________________________
Reason 2: _______________________
________________________________
________________________________
Reason 3: _______________________
________________________________
________________________________
-----------------------------------------------------------------------------------------Example 7: The diagram shows lines l, m, n, p, and q all cut by
transversal t. Which two lines are parallel? How do you know?