Answer Key
Math 302B, Section 1
Part 1: Define each term, and then draw a picture then represents each definition.
Note: All of the following definitions are not to be taken as precise definitions. Pictures are not included.
1. Point
2. Collinear Points
3. Coplanar points
4. Line
A reference to a location.
Points that lie on the same
line.
Points that lie on the
same plane.
An infinite collection of
points that indicate a
straight path.
5. Line Segment
6. Concurrent Lines
7. Perpendicular Lines
8. Skew Lines
A subset of a line. This
subset consists of two
endpoints and all of the
points in between those
endpoints.
9. Ray
Three of more lines
intersecting at a single
point.
Refer to discussion in
class.
Two lines that don’t
intersect because they
don’t lie in the same
plane.
10. Angle
11. Exterior of an angle
12. Interior of an angle
A subset of a line that
contains a specific point
(endpoint) and all of the
points on the same side.
13. Acute angle
The union of two rays that
have a common endpoint.
A portion of an angle that The intersection of the
exists
space disjoint from the
rays that create the angle.
14. Obtuse angle
15. Straight angle
16 Reflex angle
An angle that measures less
than 90 degrees.
An angle that measures
between 90 and 180
degrees.
An angle that measures
exactly 180 degrees.
An angle whose measure
is greater than 180
degrees.
17. Complementary angles
18. Supplementary angles
19. Vertical angles
20. Right angle
Two angles whose measures
sum up to 90 degrees.
Two angles whose
measures sum up to 180
degrees.
Angles that are
“opposite” each other (in
regards to location) when
two lines intersect.
An angle whose measure
is exactly 90 degrees.
21. Plane
22. Parallel Lines
An unbounded 2dimensional shape. A
surface that contains at least
three points not all in a
straight line and is such that
a line drawn through any 2
points in it lies wholly in the
surface.
Co-planar lines that never
intersect. (Note: I am only
defining parallel lines for
co-planar lines)
Part 2: Name each figure.
1.
2.
S
G
E
M
line GM
line segment MG
Ray GM
Ray MG
line SE
line segment ES
Ray SE
Ray ES
Part 3: Complete.
1.
2.
Name a pair of adjacent angles.
Name a pair of complementary
angles.
Angle TMY and Angle YMN
4.
3.
Angle ZMF and Angle FML
5.
Name a pair of vertical angles.
Angle QFC and Angle LFC
6.
Name a pair of complementary
angles.
Angle GTZ and Angle ZTB
Angle QGB and Angle EGH
Name a pair of supplementary
angles.
Name a pair of supplementary
angles.
Angle LFH and Angle HFP
Part 4: Answer each question.
1.
2.
3.
NA GX
QL KF
AED and VDN are vertical
angles.
KZH and GZF are vertical
angles.
4.
HJ ED
5.
ZUJ and HUR are vertical
angles.
6.
F
G
I
C
D
A
B
H
E
Using a protractor, determine
the measure of angle ABC.
about 126°
Angle Measure
Using a protractor, determine
the measure of angle DEF.
about 51°
Angle Measure
Using a protractor, determine
the measure of angle GHI.
about 285°
Angle Measure
Part 5: Complete using the diagram provided.
A
1
3
B
F
2
G
4
E
C
D
1. Name the line marked 3 in six different ways.
(all notations should have a double arrow over the letters): AC, CA, AB, BA, CB, BC
2. Name the line segment named 2 in two different ways.
(all notations should have a straight line over the letters): BG, GB
3. Name the angle marked 1 in four different ways.
< CAE, < BAE, < BAF, < EAC (there are different ways to name the angles than just what is listed here)
4. What is vertex marked 4?
G (note a vertex is just a point, so I was only looking for you to name a point)
5. Name the ray beginning at F and going towards A.
(the ray should have a single arrow over the letters): FA


6. Is DE = DC ? Explain.
NO. They are going in different directions and as such, contain different points. One ray contains the point C, while the other
does not.


7. Is BG = BE ? Explain.
YES. Although they use a different second letter, they both start at B and go in the same direction. Therefore, they contain the
same points.


8. Is BC = CB ? Explain.
NO. One has the endpoint of B and the other has an endpoint of C. One ray contains the point A, while the other ray does not.
9. Name the sides of
AFD.
(Note: The sides of the angle are rays and should have single arrows over the letters.) FA and FD
.
Part 6: Complete.
1. Sketch four lines such that three are concurrent with each other and two are parallel to each other.
2. True or False? Briefly justify your answer
a. If a line is perpendicular to a plane, then it is perpendicular to all lines in that plane.
TRUE. Refer to discussion in class.
b. If three lines are concurrent, then they are also coplanar.
FALSE. Refer to discussion in class.
3. Sketch a pair of angles whose intersection is
a. Exactly two points or explain why this is not possible.
b. Exactly four points or explain why this is not possible