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Honors Geometry
Review Exercises for the December Exam
Here is a miscellany of exercises to help you prepare for the semester examination. You should
also use your class notes, homework, quizzes, and tests for more exercises.
Write one of the words SOMETIMES, ALWAYS, or NEVER to complete each statement. You
need to think of all possibilities to decide which word is correct.
1.
The converse of a conditional _______________ has the ame truth value as the original
conditional..
2.
Three points are _________________ collinear.
3.
Three points are ________________ coplanar.
4.
Parallel lines are ________________ coplanar.
5.
Through two points, there is ________________ exactly one line.
6.
If two rays share a common endpoint, they are _______ opposite rays.
7.
The locus of points which are 6 inches from a point, A, _______________ is a circle
with radius 6.
8.
If same side interior angles formed from two lines and a transversal measure 1000 and
800, then the other two lines are ____________ parallel.
TRUE or FALSE?
9.
If two lines are perpendicular to the same line, then they are parallel to each other.
10.
In an orthographic drawing of a solid made of cubes, the right view and the left view are
identical.
11.
If parallel lines are cut by a transversal, then alternate interior angles could be
complementary.
12.
The supplements of congruent angles are congruent.
13.
Perpendicular is a symmetric relation.
14.
“Greater than” is transitive.
15.
Supplementary angles must be adjacent.
16.
Each interior angle of a regular hexagon has a measure of 1200.
Honors Geometry Exam Review Questions
page 2
Complete the following.
17.
An _________ is the union of two rays with a common endpoint.
18.
Perpendicular lines form ________________________.
19.
If parallel lines are cut by a transversal, then _______________________ are
congruent.
20.
In a conditional statement, if you reverse the hypothesis and conclusion, you get the
___________________ of the original statement.
21.
If an original conditional statement is false, then the _________________ of the original
statement must also be false.
22.
Examine the diagram.
True or False
a) A, B, D, and E are coplanar
b) B and C are collinear
c) A, F, and C are collinear
d) F lies in plane P

e) FC intersects plane P at point A and plane Q at
point C
F
P
A
Q
B
D
Name the following:
f) The intersection of planes P and Q
g) A pair of skew lines

h) The intersection of plane Q and FC
C
E
23.
Refer to the diagram below.
P
a)
If mPXR = 42,find the measure of these angles:
mRXT
mQXS
mSXP
b)
If RPX  SQX , then what lines must be parallel? Give
the reason.
c)
If SXQ  TQX, then what lines must be parallel? Give
the reason.
R
T
X
S
Q
Honors Geometry Exam Review Questions
24.
Write three postulates.
a.
b.
c.
25.
Write three theorems.
a.
b.
c.
Solve for any variable in the drawings.
26.
27.
28.
29.
30.
31.
page 3
Honors Geometry Exam Review Questions
page 4
32.
Make a drawing which clearly shows 3 skew lines, and one line parallel to one of the
skew lines.
33.
The vertex of an angle is at (3, 7). A(-1,5) is on one ray of the angle, and B (6,9) is on
the other ray. Calculate the measure of the angle. (Check in the Coordinate Geometry
packet for the method.)
34.
M is the midpoint of CD . The coordinates are:
C (6 , x)
M (1 , x – 4)
D (-4 , 11)
35.
Find the length of CD if C (6 , -3) and ( 0 , 8).
36.
Where is the midpoint of AQ if A(9 , 4) and Q(-1, 11) ?
37.
A line passes through the points A( -4, 5) and B(2, -7).
a)
Find AB
b)

Find the slope of AB
Honors Geometry Exam Review Questions
c)
d)
page 5

Find an equation of AB . Write your answer in point-slope form.
Find the coordinate of the midpoint of AB
Construct these with compass and straightedge.
38.
an isosceles right triangle with sides (non-hypotenuse) given.
39.
a line perpendicular to AB through C.
40.
a square with side EF.
E
F
Honors Geometry Exam Review Questions
41.
a 450 angle
42.
the complement of < A
page 6
Draw each of these.
43.
This isometric drawing has a volume of 9 cubes. Make a drawing with cubes whose
volume is 13 cubes.
\
Honors Geometry Exam Review Questions
page 7
44.
What are the loci of points which are equidistant from two points A, and B, and which
are 9 inches from a point C?
45.
If a double the size of an angle (say from 200 to 400), what happens to the supplement of
the complement of the angle?
46.
Write “Pizza is served if and only if today is Tuesday” as two “if …then …”
statements.
Write the “only if” half as an “if …then …” statement.
47.
Consider a set of n noncollinear points. Connect each point with all other points. Count
the number of line segments.
# of segments =
# of segments =
# of segments =
If there are n noncollinear points, what is an expression for the total number of segments
which can be drawn?
Honors Geometry Exam Review Questions
48.
Given: A rolling stone gathers no moss.
a)
Rewrite the statement as a conditional.
b)
Write the converse.
c)
Write a biconditional combining the statement and its converse.
d)
Assume the given statement is true. Which of these statements must be true?

This big gray stone is not rolling, therefore it is gathering moss.

That red stone is gathering moss, therefore it is not rolling.

That green stone is not gathering moss, therefore it is rolling.
Make a truth table for this logic statement: ( P  Q)  (Q ~ P)
49.
P
T
T
F
Q
T
F
T
F
F
50.
page 8
Make a conclusion (if possible) and name the pattern of reasoning.
PR
P ~ R
~ R W
(S  R)  W
a) R
b) R
c) ( S  R )
d) R  Q
 ____
____
____
____
Honors Geometry Exam Review Questions
51.
page 9
Assuming A and B are both true, P and Q are both false, and X and Y are of unknown
truth value. Determine (if possible) the truth value of each statement.
a) A  ( B  X )
b) B  ( P  A)
c) ( A  X )  ( B  Q)
52.
Write a logical expression which is logically equivalent to ( P  Q)  Q .
53.
Write the inverse of “People wear flip flops only if they hate real shoes.”
54.
Give an example of a syllogism.
55.
Give an example of the law of disjunction.
56.

Draw two horizontal planes, A and B, a vertical plane, C, and a line DE so that D lies in C,
and E lies in A.
Honors Geometry Exam Review Questions
57.
page 10
Which lines (if any) must be parallel?
d
6
a) 1  2
b) 6  7
c) 9  4
d) 10  11
e) 11  8
f) 5 and 11 are supplementary
g) 4 and 12 are supplementary
h) 5 and 10 are supplementary
1
a
b
2
12
c
58.
Assume that a || b and c ||d (drawing above right)
m< 1 = 960
m < 6 = 400
Calculate all of the other numbered angles.
9
5 10
11
3
8
4
7
Honors Geometry Exam Review Questions
page 11
59.
What is the locus of the center of a sphere that rolls around on a rectangular table top
whose surface measures 5 feet by 3 feet?
60.
What are the loci of points that are equidistant from two points, A and B and also
equidistant from two parallel planes?
61.
a)
What is the locus of points, in a plane, which are equidistant from two perpendicular
rays which have a common endpoint?
b)
What is the locus of points which are equidistant from two perpendicular
rays which have a common endpoint
Proofs.
62.
Given: BA  BC , < 1  < 3
Prove: <2 is comp to < 3
63.
Given: a || b , < 1  < 3
Prove: c || d
64.
Given: < 1  < 4
Prove: < 2  < 3
Honors Geometry Exam Review Exercises
65.
Given: < DAB  < DBA
<2  <3
Prove: < 1  < 4
Calculate the areas.
66.
67.
page 13
Honors Geometry Exam Review Exercises
68.
69.
70.
71.
72.
1
h (b1  b2 )
2
Show why this formulas should be true.
(i.e., drive the formula)
The area of a trapezoid is A =
page 14
A figure is drawn on lattice paper
(dot paper) with 4 interior point and
11 points on its boundary. What is
its area?