1
Worksheet#1: Points, Lines, Line segments, Rays, Planes and Angles.
1) Classify each figure as a point, line, segment, ray, angle or plane. Then name each figure in as many ways as
possible.
a)
b)
c)
A

B
D
POINT
G
C
h
F
E
LINE
PLANE
Classification: _________________
Classification: _________________
Classification: ________________
Name(s): ____________________
Name(s): ____________________
Name(s): ____________________
_____________________
_____________________
d)
e)
H
M
f)
P
L
J
S
K
N
LINE SEGMENT Classification: _________________
RAY
ANGLE
Classification: _________________
Name(s): ____________________
Name(s): ____________________
_____________________
_____________________
Classification: _________________
Name(s): _____________________
______________________
T
2) Use words to describe the figure in as much detail as possible:
X
Q
W
U
Geometry Assignment Chapter 1
S
2
E
3)
H
a) Name all the points NOT on plane D.
b) Name a line on plane B.
M
D
C
G
c) Name 4 coplanar points.
d) Name 3 collinear points.
L
B
K
l
e) What is another name for plane D?
f) Name the intersection of plane B and MC .
g) Name a line that intersects MC .
4) Draw and label a figure for each relationship.
a) line a intersects plane K at P.
c) WV and EC are coplanar, but do not intersect.
Geometry Assignment Chapter 1
b) R and Y lie on PL .
3
A
B
C
D
5) Using a box on top of the table as modelled by our diagram:
a) Name two planes that seem to intersect.
W
b) Name two planes that do not seem to intersect.
E
R
S
R
c) Name the intersection of plane ABC and plane WER
d) Name the intersection of plane ADW and plane AWB. (written: plane ADW  plane AWB)
e) Find: WR  RS (this symbol means to find the intersection between the two lines)
f) How many planes appear in the entire figure?
g) Name 4 points that are NON-coplanar.
6) Using the room you are currently in, which part of the room would represent/model …
a) a plane?
b) a point?
7) Describe what you see using words and symbols. {Need to use both words and symbols}
W
a)
b)
Z
W
X
L
P
Y
Geometry Assignment Chapter 1
B
U
R
R
4
R
8) Using the diagram, answer the following questions about the
I
P
Hexagonal prism on top of a table shown to the right.
S
M
W
a) How many planes are shown in the figure?
X
b) Name a plane that appears parallel to plane HXG
N
A
E
G
H
O
c) Name 4 planes that intersects plane SMO.
d) Name a point coplanar with R,P and M.
e) Name a plane that parallel to plane HOM.
f) Name a segment that appears parallel to OG
g) Name all points non-coplanar to plane N.
h) Find plane AGS  plane MOG.
i) Find plane PWH  plane RIA.
j) Which segment appears to be skew with HO (circle all that apply) XE , PE , PR , IR
9) Write a description for each figure:
a)
R
a
W
K
Geometry Assignment Chapter 1
5
Worksheet #2: Betweenness and congruent segments.
10) Review your Algebra:
a) Solve: 3x + 6 = 8x – 14
b) Solve: (4x) + (2x – 7) = 7x – 10
20 = 5x
6x – 7 = 7x - 10
x=4
3=x
c) Solve: y 2  25  0
(y – 5)(y+5) = 0
or
d) Solve: m2  5m  14  0
y 2  25
(m – 2) (m + 7) = 0
y 2   25
{zero product property}
y  5
m – 2 = 0 or m + 7 = 0
m = 2 or m = -7
y = 5 or -5
11) Draw a picture to match the written description: “Point B is between points R and T.”
R
T
B
B
a) Are the three points collinear or non-collinear?
b) True or False: RB + BT = RT
c) True or False: RB = BT
12) Draw a picture to match the written description: Point H is not between F and G.
H
F
Geometry Assignment Chapter 1
G
6
13) Find the length of HG.
a) GK  7.4 cm
4.6
HK= 12 cm
H
K
G
19.4
b) GK  7.4 cm
c) GK  4
3
cm
5
HK= 12 cm
H
HK= 7 cm
H
K
2
2
5
G
K
11
d) GK  4
3
cm
5
HK= 7
1
cm
3
G
H
14
15
or
179
15
G
K
14) Find the length of YT. (The length is just denoted as YT, without anything above it)
YR= 2x
RT= 3x + 6
YT = 7x - 4
31
2x + 3x + 6 = 7x – 4
Y
T
R
X=5
15) Draw and label a diagram to represent: M is between J and K. MJ = 6.6ft
JK = 7.1ft.
Find the length of MK. 7.1 – 6.6
16) Y is between C and D. CD = 2x + 10 YC = 3x – 9, YD = x + 5. Justify whether YC  YD .
3x – 9 + x + 5 = 2x + 10 CY = 3(7)-9 = 12
4x – 4 = 2x + 10
2x = 14
YD = 7 + 5 = 12
Yes, since CY has the same length as YD, they are congruent.
X=7
Geometry Assignment Chapter 1
0.5
7
17) Given: MC  CN
MC = 4x – 3 and CN = x + 9, find the length of MC.
MC = 4(4)-3 = 13
4x – 3 = x + 9
3x = 12
X=4
18) What is wrong with this picture? Given: MC  CN
MC = 3 - 4x and CN = x - 7
3 – 4x = x – 7
If x = 2, MC = 3 – 4(2) = 3 – 8 = -5
10 = 5x
The length of a side cannot be negative.
2=x
19) How do we show congruent segments on a diagram?
Use tick marks (same picture…)
20) Determine which pair of segments are known to be congruent to each other.
H
W
a)
E
HN  EX
HE  GO
N
X
b)
T
4 cm
P
G
R
TP  RA
4 cm
A
O
21) If point K is between T and R, explain (in words) how you can find TR if you know TK and KR.
If K is between T and R, then T, K and R are collinear, which means TK + KR = TR. So, we can just add
up the segments that we know to find the total length.
Geometry Assignment Chapter 1
8
22) R is between Y and T: YR= x 2  2 x
RT=10x
YT=28 (This was a typo… was 25)
YR + RT = YT
x 2  2 x  10 x  28
x 2  12 x  28  0
( x  2)( x  14)  0
x  2 or x = -14
23) Multiple Choice: In the figure, points A, B, C D and E are collinear. If AE = 27, BD = 11, and BC  CD  DE ,
what is AD?
A. 9.5
A
B. 16
C. 10.5
D. 21.5
B
C
D
E
2
24) Multiple Choice: If g ( x)  3x  5 x , find the value of f(-2)
A. 22
B. 12
C. -2
25. Evaluate: m  n if m = 3 and n = -7.
26. Evaluate: a 2  b 2 if a = 5 and b = 12.
Geometry Assignment Chapter 1
D. 2
9
Worksheet #3: Pythagorean Theorem, Distance Formula, and Midpoints.
27) Simplify each radical expression, then find the approximate value to the nearest hundredth.
a)
b)
50
72
36 2
25 2
6 2
5 2
28) Use the Pythagorean Theorem to find the length of the unknown side.
a)
b)
?
3m
5
?
7m
25
24 m
4m
c)
d)
10 ft
4 ft
?
4  x  10
2
2
2
16  x 2  100
x 2  100  16
x 2  84
x  84  4 21  2 21
Geometry Assignment Chapter 1
?
12 ft
10 ft
102  x 2  122
100  x 2  144
x 2  144  100
x 2  44
x  44  4 11  2 11
10
29) Given the diagram, form a right triangle using the segment joining the two marked points as the hypotenuse.
Label the lengths of each leg of the triangle. Use the Pythagorean Theorem to find the length of the
hypotenuse.
42  52  AB 2
a)
16  25  AB 2
4
41  AB 2
5
41  AB
b)
6 2  52  AB 2
36  25  AB 2
61  AB 2
6
61  AB
5
c)
7 2  32  AB 2
49  9  AB 2
58  AB 2
58  AB
3
7
Geometry Assignment Chapter 1
11
30) Use the distance formula to determine the distance between the two given points.
a) K(-2, 5) and P(3,1)
b) J(-8,1) and R(-3,-5)
D  (2  3) 2  (5  1) 2
D  (8  3) 2  (1  5) 2
D  (5) 2  (4) 2
D  (8  3) 2  (1  5) 2
D  25  16  41
D  (5) 2  (6) 2  25  36  61
c) W(-4,-2) and H(3,-5)
D  (4  3) 2  (2  5) 2
D  (7) 2  (2  5) 2
D  49  9  58
31) Use the midpoint formula to determine the coordinates of the midpoint of the two given points.
Graph the original points and then the midpoint you found (to see if it makes sense)
a) W(4, 7) and A(-2, 1)
 4  2 7  1 
Midpoint= 
,
  1, 4 
2 
 2
b) L(-5,-6) and Y(-2, 3)
 5  2 6  3   7 3 
Midpoint= 
,
   ,   (3.5, 1.5)
2   2 2 
 2
Geometry Assignment Chapter 1
12
32) Find the missing endpoint, given the coordinates of one endpoint and the coordinates of the midpoint .
a) A( 3, 6) and Midpoint (0,0)
(-3,-6)
b) C(-2,4) and Midpoint (-3, 1)
(-4,-2)
c) A( -3, 6) and Midpoint (1,0)
(5, -6)
d) C(-6,-4) and Midpoint (-3, 1)
(0,6)
Geometry Assignment Chapter 1