Download Name the Relationship

Teacher: Mr. Joseph
Name:__________________________
Parallel Lines and Transversals
Period: ________ Date: ____________
Name the Relationship (if any):
1)
2)
Name the relationship:
7 and
1
3)
Name the relationship:
6 and
1
Name the relationship:
1 and
3
4)
Name the relationship:
4 and
1
Solve:
5)
6)
If c // d, what is the relationship
between m 16 and m 3?
If c // d, and m 6 = 67°, what is m
12?
7)
8)
If m // p, what is the relationship
between m 7 and m 5?
This drawing shows an apparatus
designed to divert light rays around an
obstacle. The light comes in on line m,
reflects off of line a, then reflects off of
line b and ends up on
line n. a // band m // n. Furthermore,
because the angle of incident equals the
angle of reflection, 2
4and
7
10. m 3 = 154°, what is m 8?
List all Parallel Lines:
9)
10)
If
1
If
6?
11)
2
7?
12)
If
7 and
9 are supplementary?
If m 2 = 25° and m 11=25°?
EasyWorksheet Step By Step Answers
User Name: J. Joseph
Form #9191372842
Practice Problems
1)
Name the relationship: 7 and 1
First, let's identify our transversal: Line q
Notice the angles are outside the two lines (line r and line t), but are on different sides
of line q.
This means they are "Alternate Exterior".
2)
Name the relationship: 6 and 1
Since we cannot apply any of the following relationships in this case:
Vertical Angles
Linear Pair
Alternate Interior
Alternate Exterior
Consecutive Interior
Corresponding
We need to conclude that there is no name for this relationship.
3)
Name the relationship: 4 and 1
Notice that the angles are next to each other on a little cross (the other intersection(s)
do not matter!), so our answer is "Linear Pair"
4)
Name the relationship: 1 and 3
First, we need to identify our transversal as line h.
Notice that the angles are in the same position on two different crosses?! (Example:
top right corner).
If you have trouble seeing this, cover up everything except for the two intersections
that we are looking at!
This means the angles are "Corresponding".
5)
If c // d, what is the relationship between m 16 and m 3?
First, don't forget that // means parallel, and in the case of parallel lines and a
transversal, all angles are known if one angle is known.
In this case, the angles alternate, so m 1 = m 7 = m 8 = m 14 and m 2 = m 3 =
m 9 = m 10.
And any other combinations of these angles are supplementary (add to 180°).
AND, m 4 = m 11 = m 13 = m 16 and m 5 = m 6 = m 12 = m 15.
And any other combinations of these angles are supplementary (add to 180°).
However, angles #1, 2, 3, 7, 8, 9, 10, and 14 have nothing to do with angles #4, 5, 6,
11, 12, 13, 15, and 16, since we only have c // d.
So we get no relation for our answer.
6)
If c // d, and m 6 = 67°, what is m 12?
First, don't forget that // means parallel, and in the case of parallel lines and a
transversal, all angles are known if one angle is known.
In this case, the angles alternate, so m 1 = m 7 = m 8 = m 14 and m 2 = m 3 =
m 9 = m 10.
And any other combinations of these angles are supplementary (add to 180°).
AND, m 4 = m 11 = m 13 = m 16 and m 5 = m 6 = m 12 = m 15.
And any other combinations of these angles are supplementary (add to 180°).
However, angles #1, 2, 3, 7, 8, 9, 10, and 14 have nothing to do with angles #4, 5, 6,
11, 12, 13, 15, and 16, since we only have c // d.
So we get 67° for our answer.
7)
If m // p, what is the relationship between m 7 and m 5?
First, don't forget that // means parallel, and in the case of parallel lines and a
transversal, all angles are known if one angle is known.
In this case, the angles alternate, so m 1 = m 2 = m 3 = m 4, and m 5 = m 6 =
m 7 = m 8.
And any angles that are not listed as equal are supplementary (add to 180°). In this
case, the angles are congruent.
So we get congruent for our answer.
8)
This drawing shows an apparatus designed to divert light rays around an
obstacle. The light comes in on line m, reflects off of line a, then reflects off of
line b and ends up on line n. a // b and m // n. Furthermore, because the angle of
incident equals the angle of reflection, 2
4 and 7
10. m 3 = 154°, what
is m 8?
3
6 because they are alternate interior angles.
So m 6 = 154°
Since 7, 10, and 6 all lie on a line, they sum to 180° (This is the Angle Addition
Postulate)
And since 10
7, we will let m 10 = m 7 = x.
m 6 + m 7 + m 10 = 180°
154° + x + x = 180°
2x = 26°
m 7 = m 10 = 13°
8
10 because they are vertical angles.
So we have m 8 = m 10 = 13°
9)
If 1
6?
There are two cases to consider: a // b and c // d.
In this case, if c // d, then the angles alternate, so m 1 = m 8 = m 7 = m 14, m 3
= m 2 = m 9 = m 10 , m 4 = m 11 = m 13 = m 16, and m 5 = m 6 = m 12
= m 15
And, if a // b, then the angles alternate, so m 1 = m 7 = m 4 = m 11, m 3 = m 2
= m 5 = m 6 , m 8 = m 14 = m 13 = m 16, and m 9 = m 10 = m 12 = m 15
But don't forget, in order for two lines to be parallel, we must have the angles located
at two DIFFERENT intersections.
In this case, this does not hold, so there is no relation.
So we get None for our answer.
10)
If 2
7?
In this case, if t // r, then the angles alternate, so m 1 = m 2 = m 3 = m 4, and m
5 = m 6 = m 7 = m 8.
But don't forget, in order for two lines to be parallel, we must have the angles located
at two DIFFERENT intersections.
In this case, this does not hold, so there is no relation.
So we get None for our answer.
11)
If 7 and 9 are supplementary?
There are two cases to consider: a // b and c // d.
If c // d (with a as the transversal), then the angles alternate, so either 2 or 3 is
supplementary to either 8 or 14, and either 1 or 7 is supplementary to either 9
or 10
And if c // d (with b as the transversal), then the angles alternate, so either 4 or 11
is supplementary to either 12 or 15, and either 5 or 6 is supplementary to
either 13 or 16
While, if a // b (with c as the transversal), then the angles alternate, so either 2 or 3
is supplementary to either 4 or 11, and either 1 or 7 is supplementary to
either 6 or 5
And finally, if a // b (with d as the transversal), then the angles alternate, so either 8
or 14 is supplementary to either 12 or 15, and either 9 or 10 is supplementary
to either 13 or 16
But don't forget, in order for two lines to be parallel, we must have the angles located
at two DIFFERENT intersections.
In this case, the two given angles are in the appropriate relationship, so c // d is our
answer.
So we get c // d for our answer.
12)
If m 2 = 25° and m 11=25°?
There are two cases to consider: a // b and c // d.
In this case, if c // d, then the angles alternate, so m 1 = m 8 = m 7 = m 14, m 3
= m 2 = m 9 = m 10 , m 4 = m 11 = m 13 = m 16, and m 5 = m 6 = m 12
= m 15
And, if a // b, then the angles alternate, so m 1 = m 7 = m 4 = m 11, m 3 = m 2
= m 5 = m 6 , m 8 = m 14 = m 13 = m 16, and m 9 = m 10 = m 12 = m 15
But don't forget, in order for two lines to be parallel, we must have the angles located
at two DIFFERENT intersections.
In this case, this does not hold, so there is no relation.
So we get None for our answer.
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