Name: _________________________
Basics and Proofs
Create Vocabulary Cards
See the example cards which follow:
Definition:
a part of a line with two
endpoints; has measure
EX. 1
Notation:
AC or CA
 Only use two endpoints
line segment
Real-life objects:
pencil, piece of dry
spaghetti, flag pole
Drawing:
B
A
Definition:
two angles that share a
common vertex and a
common side, but no
common interior points
C
Example:
1
2
1 and 2 are adjacent angles
EX. 2
adjacent angles
Relationship:
All linear pairs are adjacent
angles.
Non-example:
1
2
1
Definition:
Example:
Definition:
Point
Real Life Example:
Definition:
Line
Notation:
Example:
Real Life Example:
Definition:
Plane
Real Life Example:
Example:
Notation:
Example:
Line Segment
Notation:
Real Life Example:
Notation:
2
Definition:
Example:
Definition:
Ray
Real Life Example:
Definition:
Angle
Notation:
Example:
Real Life Example:
Definition:
Notation:
Example:
Perpendicular
Lines
Parallel Lines
Relationship:
Example:
Notation:
Relationship:
Notation:
3
Definition:
Example:
Definition:
Plane
Real Life Example:
Definition:
Congruent
Notation:
Example:
Relationship:
Definition:
Notation:
Example:
Linear Pairs
Angle Bisector
Relationship:
Example:
Notation:
Relationship:
Notation:
4
Definition:
Example:
Definition:
Adjacent Angles
Vertical Angles
Relationship:
Definition:
Relationship:
Example:
Definition:
Supplementary
Angles
Relationship:
Example:
Notation:
Example:
Complementary
Angles
Example:
Relationship:
Example:
5
Points, Lines, and Planes:
POINTS

Dimensionless meaning NO SIZE OR SHAPE

Labeled with a CAPITAL LETTER
LINES

Only ONE dimension

It takes TWO points to determine a line
Naming Lines
o Use any TWO LETTERS that lie on the line in any order with this symbol
above the two letters
o Use ONLY the cursive letter LABEL with the word line instead of symbol
Example: Name the following lines in as many ways as you can:
A
B
m
!!!YOU SHOULD NEVER MIX POINTS WITH THE LABEL WHEN NAMING!!!
INTERSECTING LINES

Two lines intersect at a SINGLE POINT
YOU SHOULD ALSO BE ABLE TO SKETCH OUT CERTAIN SITUATIONS:
Example: Draw lines m and n intersecting at point X
6
Collinear just means in points that are ON THE SAME LINE
Example: Which of the following points are collinear?
A
W
F
Y
LINE SEGMENTS
o Naming: Always use TWO ENDPOINTS (Never use middle points in name)
o Use this symbol above the TWO endpoints
Example: Name the following segments:
J
K
L
P
Q
M
RAYS

Have a defined INITIAL OR STARTING point

Real world example: RAY OF LIGHT
Naming Rays

Draw the symbol POINTING TO THE RIGHT (No matter which way it points)

Always name the INITIAL POINT first, then use any other point that lies in the
direction the ray points

You will use ONLY TWO POINTS when naming a ray (No matter how many shown)
Example: Name the following rays as many ways as you can:
D
E
F
7
Practice
Name the following as many ways as you can:
A
A
B
B
B
C
A
B
m
B
A
B
B
A
A
m
C
C
B
C
A
Sketch the following:
Parallel lines m and n
Line AB Intersecting Line
Ray AB
CD at Point X
Ray BA
Opposite Rays BA and BR
Pair of Rays Intersecting
at More than One Point
Line Segment AB which
3 Points which are NON-
A Line that Can be named
also contains Point C
COLLINEAR
with a Single Letter
8
Practice:
Name each line in two different ways.
1.
m
B
2.
3.
R
L
F
M
J
P
k
Name each of the following:
4.
5.
J
6.
A
I
L
D
N
A
B
7.
P
8.
J
S
E
9.
E
D
W
B
K
L
10. Use a protractor to measure the following angles:
W
A
B
B
K
L
9
Use a ruler to draw each of the following:
11. FM
12. SW
14. BIG
13 . SF
15 COS
16. Plane RJP
17. Draw segment JW, point W has coordinates (2, -5)
and J(-3, 4).
18. Draw ray LB with endpoint L(2,0) that goes through point
B(-3,-6).
19. Name the angles that may be named by one letter using the vertex point.
J
A
O
S
N
20. Draw a figure that contains at least three angles which all require naming with three letters
10
Name: ________________________________ Hour: ___________________
1. Complete the following statements:
a. It takes ________ points to determine a line.
b. Two lines intersect at a _________________
c. Opposite rays create a ___________________
2. Give at least three names for each of the following figures:
m
a.
A
C
A B
b.
C
c.
R
A
D
T
3. Name each of the following figures:
a.
A
R
m
b.
c.
R
A
B
4. Name a pair of opposite rays shown below:
A
B
C
D
11
PLANES
P

Flat surfaces such as A TABLE TOP

Extends infinitely in BOTH dimensions

It takes 3 NON-COLLINEAR points to determine a plane
H
G
I
NAMING PLANES:

Use the LABEL (Just like a label on a line but a capital letter)

Use any THREE NON-COLLINEAR points

There is NO SYMBOL for planes so you write the word “Plane XYZ”

Don’t MIX the label with the points in the name
Example Problem: Name the following plane as many ways as you can:
R
S
T
W
DETERMINING WHETHER POINTS ARE COPLANAR:

Any 3 points given are ALWAYS coplanar

If asked whether 4 points are coplanar
o The points make a Parallelogram-YES!
o Parallelogram not possible-NO!

If told to name the point coplanar to others, COMPLETE THE PARALLELOGRAM
B
C
Example Problem: Are the following points coplanar?:
A, B, F and D?
A, B, F and E?
D
A
A, D, F and G?
G
F
Example Problem: Name the point that is coplanar w/:
F, G and H?
B, C and F?
E
H
12
INTERSECTING PLANES:

Two planes intersect at A LINE

Think of where TWO WALLS would meet (It is NOT just a single POINT)
Example Problem #7: Name the intersection of the given planes:
ABC and DEF
A
B
C
D
F
E
PARALLEL AND SKEW LINES:

G
Parallel lines lie on the same plane and will never cross
H
o Real world examples:

Skew lines do not lie on the same plane and have the following properties:
o Skew lines do not INTERSECT (Cross)
o Skew lines are not PARALLEL
B
Example Problem: Name all segments skew to AB:
C
D
A
G
F
E
H
Example Problem: Name all segments parallel to AE
13
R
Practice
Q
Q
C
Part 1:
1. Are N, P, Q, and R coplanar? _______
N
2. Are N, J, P, and Q coplanar?______
A
3. Are N, M, and L coplanar?_______
P
L
M
Part 2
J
4. Name plane P in another way.____________


5. What is the intersection of ST and TR ?___________

6. What is the intersection of TR and plane P? __________
K
S
7. Are points S, T, and R are collinear? _______
8. Points S, T, and R are contained in Plane P? ________,
9. Points T, R, and Q are contained in Plane P? ________.
Q
P
Part 3: Tell whether the lines are intersecting, parallel, or skew.
B
10.
11.
12.
13.


AE and BF _________


FG and BC ________


CD and BF ________


DC and EF ________
R
T
C
D
A
G
F
E
H
Part 4: Complete with always, sometimes, or never to make a true statement.
14. A line and a point not on the line are ___________ coplanar.
15. Four Points are ___________ coplanar.
16. Two planes ___________ intersect in exactly one point.
17. Intersecting lines are _______________ coplanar.
18. Three points are _______________ coplanar.
14
Name: ______________________
ANGLES
o Created by 2 _________________
o The shared initial point is referred to as the _________________
o Naming

Always use _________________if vertex is shared

Can use _________________if vertex is not shared

If you have to use three letters, put the vertex ______________
Example Problem #11: Name the following angle as many ways as you can:
F
A
R
B
C
V
o MEASURING AN ANGLE

Use an instrument called a _____________

The most important thing is to first line up the ______________

Line EITHER of the sides of the angle with the flat “zero line” on the
protractor

Measure the angle using the other side of the angle
STUDENTS ALWAYS GET CONFUSED BY THE FACT THAT THERE ARE 2
ROWS OF NUMBERS ON A PROTRACTOR!
1. IF THE “ZERO” IS AT THE TOP, USE THE TOP ROW OF NUMBERS
2. IF THE ZERO IS AT THE BOTTOM, USE THE BOTTOM ROW
3. USE This Trick:
IF IT IS BIGGER THAN AN “L”, PICK THE NUMBER GREATER THAN 90
IF IT IS SMALLER THAN AN “L”, PICK THE ONE SMALLER THAN 90
Example Problem #12: Give the measurements of the following angles
15
Practice: Angles and Angle Measurement
Angle Measurement Activity: A Protractor Treasure Hunt
Find the measure of each angle using your protractor.
1
3
4
6
5
C
B
D

8
A

7
9
E

10

O
11.
m  AOD =
12.
m  DOB =
13.
m7 + m8 =
14.
m  AOE - m  COE =
____
16
Practice
Create angles using given measurements: (Hint: Start with a vertex and one flat ray)
100˚
45˚
135˚
17
Practice
1.
Name: ________________ Hr:___
Name the sides of the Angle
Name the vertex of the Angle
Give three names for the Angle:
Draw the following figures:
2. ABC=45 degrees
3. COS=100 degrees
4. XYZ=150 degrees
5. Find the measure of the following angles:
a)
b)
6. Vocabulary Practice:
a) An angle is formed when two ____________ share their initial point
b) The shared initial point is called the _____________
c) You can name an angle with ___________ letters if the angle is by itself
d) You have to use __________ letters if the vertex is shared
e) When naming an angle with three letters, the ____________ goes in the middle
f) Two adjacent angles which add up to 180 degrees are called ________________
g) Intersecting planes intersect at a _______________
h) Points are dimensionless meaning that they have no _______________
i) It takes _____________________ points to determine a plane
j) When naming a ray, always name the __________________ first
k) When naming angles, the __________________ always goes in the middle
18