Name: ______________
5-3 Non Parallel lines and Transversal
Notes
____________ _______________ angles: angles created by intersecting
lines that share only a vertex
_______________: a line that intersects two or more lines
__________________ angles: angles that occupy the same relative
position in two different intersections
<1 and <5 are corresponding angles
<3 and <7 are corresponding angles
There are 2 more pairs
_____________ __________ angles: angles in opposite positions between
two lines intersected by a transversal
_____________ angles on the __________ _______: In the following
diagram, two interior angles on the same side of the transversal have been
highlighted.
Name: ______________
_______________ _____________ angles: angles in opposite positions
outside two lines intersected by a transversal
______________ angles on the __________ __________: Two exterior
angles on the same side of the transversal are highlighted in the diagram
below.
Examples:
1) In the following diagram, identify each of the following, and specify which
lines and transversals you are using.
a) an interior angle on the same side of the transversal as <6
b) an angle corresponding to <2
c) an angle corresponding to <4
d) an alternate interior angle to <4
2) In the diagram below,
a) measure and record the size of <1.
b) Identify pairs of equal angles, and find their size.
Name: ______________
If two lines intersect:

vertically opposite angles are equal
If two parallel lines are intersected by a transversal:

the alternate interior angles are equal;

the corresponding angles are equal; and

the interior angles on the same side of the transversal are
supplementary.
1) Consider the diagram below, in which l1 is parallel to l2. What are the
measures of the three indicated angles? Explain how you reached your
answers.
Angle
<1 = ______
Reason
_________________________________________
<2 = ______
_________________________________________
<3 = ______
_________________________________________
2) Given the diagram below, identify all the pairs of parallel lines and explain
your selection. (there are 2 pairs of parallel lines)
Name: ______________
5-3 Non Parallel lines and Transversal
Assignment
1) In the diagram below, identify the relationship between each pair of
angles.
a) <7 and <8
b) <2 and <7
c) <1 and <6
d) <5 and <7
2. Given the diagram below, identify the following angles.
a) an alternate exterior angle to <2
b) an interior angle on the same side of the
transversal as <7
c) an alternate interior angle to <4
d) an angle corresponding to <5
3. Identify each of the following angles. Name the two lines and the
transversal you are using.
a) two angles corresponding to <1
b) an int angle on the same side of the
transversal as <10
c) an alterate interior angle to <5
d) two int angles on the same side of the
transversal as <8
Name: ______________
4. In the diagram below, l1 is parallel to l2. State the measures of the
indicated angles and explain your reasoning.
Angle
Reason
<1 = ________
___________________________________________
<2 = ________
___________________________________________
<3 = ________
___________________________________________
<4 = ________
___________________________________________
5. What are the measures of the interior angles in the trapezoid shown
below? (Hint: Be careful of the order in which you calculate the angles.)
Angle
<1 = ___________
<2 = ___________
6. Find a pair of parallel lines in the following diagram. On the diagram, mark
all the angles necessary to determine
this. (only need to find 1 pair)
Name: ______________
7. A plumber must install pipe 2 parallel to pipe 1. He knows that <1 is 53°.
What is the measure of <2?
<2 = ___________
8. What size must <1 be if l1 is parallel to l2?
<1 = _________
9. In the diagram below, if the side of the house and the side of the shed
are parallel, what are the measures of <1 and <2?
Angle
<1 = __________
<2 = ___________
10. Given the diagram below, where l1 is parallel to l2, find the measures of
the indicated angles and state your reasons.