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Honors Geometry
Chapter 2 Practice Test
1. Make a conjecture about the next item in the sequence and then state whether you used inductive or deductive
reasoning.
L3.1.1
1, 4, 9, 16,
25 - inductive
2. Make a conjecture based on the given information and then state whether you used inductive or deductive reasoning.
L3.1.1
Lines l and m are perpendicular.
L and m form a right angle - deductive
3. Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
Given: B is between A and C
G1.1.6 and L3.3.2
Conjecture: B is the midpoint of AC
False – B does not have to be exactly on the middle of A and C.
C
A B
Use the following statements to write the statements in numbers 4 - 7. Then find its truth value.
p: an equilateral triangle has 3 congruent angles
q: an acute angle cannot measure 92°
r: 5 points are never collinear
s: A decagon has 10 sides.
4. q or s
G1.1.6 and L3.2.2
an acute angle cannot measure 92° or a decagon has 10 sides - true
5. ~p v q
G1.1.6 and L3.2.2
an equilateral triangle does not have 3 congruent angles or an acute angle cannot measure 92° - true
6. s   p ~ r 
G1.1.6 and L3.2.2
A decagon has 10 sides, and an equilateral triangle has 3 congruent angles or 5 points are sometimes collinear - true
7.
~(r  ~s)
5 points are never collinear or a decagon has 10 sides - true
G1.1.6 and L3.2.2
Honors Geometry
Chapter 2 Practice Test
In numbers 8 and 9, write the converse of the conditional statement. Determine whether the converse is
true or false. If it is false, find a counterexample.
8. Every square is a polygon
L3.2.1 and L3.2.4
If a figure is a polygon, then it is a square. False, it could be a triangle.
9. If a person is a math teacher, then they are good at geometry.
L3.2.1 and L3.2.4
If a person is good at geometry, then they are a math teacher. False – architects are good at geometry too.
In 10 and 11, write the inverse of the conditional statement. Determine whether the inverse is true or
false. If it is false, find a counterexample.
10. All triangles are figures.
L3.2.1 and L3.2.4
If a figure is not a triangle, then it is not a figure. False, it could be a rectangle which is a figure.
11. If an animal is a fish, then it swims.
L3.2.1, L3.2.3 and L3.2.4
If an animal is not a fish, then it does not swim. False, a duck is not a fish and it swims.
In 12 and 13, write the contrapositive of the conditional statement. Determine whether the
contrapositive is true or false. If it is false, find a counterexample.
12. If I do not try hard, then I will not be successful.
If I am successful, then I tried hard. True.
L3.2.1 and L3.2.4
13. Every animal is a dog.
L3.2.1, L3.2.3 and L3.2.4
If it is not a dog, then it is not an animal. False, it could be a giraffe.
14.Write a statement that will always have the same truth value as the conditional statement below.
L3.2.1 and L3.2.4
If we have school, then it must not be Sunday.
If it is Sunday, then we must not have school (the contrapositive will always have the same truth value as a conditional
statement ie they will be functionally equivalent.
Honors Geometry
Chapter 2 Practice Test
15. Doc and Marty were studying what happens when a fair spinner is spun a large number of times. Marty predicted that
they would probably get more “big” number s than small since they were experimenting late in the month. Doc tried
to say that a fair spinner will land on all numbers approximately the same number of times. Who was using
statistical reasoning?
Doc
16. When making statements in a mathematical proof, what kind of arguments are considered valid?
L3.1.1 and L3.1.2
logical deductive
17. Identify the negation of the given statement, “There exists a rectangle that is not a square.”
L3.2.3
No rectangle is not a square –or- all rectangles are squares
18. Which type of statements are proven true?
L3.1.3
theorem
19. Identify a counter example to the statement that all bikes have 2 wheels.
L3.1.3 and L3.3.2
a tricycle has 3 wheels
20. Given the true statement, “If it is snowing, then it is cold.” Which is the sufficient condition for the
statement?
L3.3.3
it is snowing (the hypothesis is sufficient)
21. Given the true statement, Two angles are congruent iff they have equal measure, which is the best way to
describe the statement, two angles have equal measure?
L3.3.3
necessary and sufficient because the full statement is a bi-conditional.
Honors Geometry
Chapter 2 Practice Test
22. Write a 2 column proof:
(G1.1.1)
Given: AOC and COB form a linear pair
Prove: m AOC + mCOB = 180
1. AOC and COB form a linear pair
2. AOC is supplementary to COB
3. mAOC + mCOB = 180
1. given
2. linear pair postulate
3. Definition of supplementary angles.
23. If a figure is reflected over 2 parallel lines, then the composite of reflections is best described as a …
G3.1.3
translation twice the distance between the parallel lines.
24. Figure F is reflected over two intersecting lines that form a 135º. Describe the isometry that results as
completely as possibly.
G3.1.3
a rotation with magnitude 90°
25. Construct a truth table for the statement, p  ~q in the space below.
L3.2.2
p
True
True
False
False
q
True
False
True
False
~q
False
True
False
True
p~q
False
True
True
True
26. Construct truth tables for the statements ~  p  q  and ~ p  ~ q , then state whether they are functionally equivalent.
L3.2.2
p
True
True
False
False
q
True
False
True
False
They are not functionally equivalent
~p
False
False
True
True
~q
False
True
False
True
p and q
True
False
False
False
~(p and q)
False
True
True
True
~p and ~q
False
False
False
True
Honors Geometry
Chapter 2 Practice Test
27. Given the statements below, explain all the possibilities that make the expression (p or q) and (r or s) true.
p: you do your homework
L3.2.2
q: you cook spaghetti
r: you feed the dog
s: you go to a movie
you do your homework and you feed the dog
you do your homework and go to a movie
you cook spaghetti and you feed the dog
you cook spaghetti and go to a movie
28. Given the diagram below in which 1  7 and 3  9, prove 1  5.
G1.1.1, G1.1.6 and L3.3.1
1
6
3
2
7
8
1. 1  7 and 3  9
2. 3  7 and 9  5
3. 1   5 (1  7  3  9  5)
4
9
5
10
1. Given
2. Vertical Angle Theorem
3. Transitive Property of Congruence
qed
Honors Geometry
Chapter 2 Practice Test
29. Determine the image of AB under the composite of reflections over l, m and then n. Describe the
isometry relating the original pre-image to the final image.
G3.1.1 and G3.1.3
F’
F
n
m
l
this is a translation and a reflection otherwise known as a walk or a glide reflection.
30. Determine the measure of 1 in the figure below.
G1.1.1
1
2
2x -2x - 12
x2 -8x + 4
2x2 -2x -12 = x2 – 8x + 4
x2 + 6x – 16 = 0
(x + 8)(x – 2) = 0
x = -8 or x = 2
if x = -8: 2(-8)2 – 2(-8) – 12 = (-8)2 –8(-8) + 4 = 132 which means m1 = 180 – 132 = 48
if x = 2: 2(2)2 -2(2) – 12 = (2)2 -8(2) + 4 = -8 (extraneous because an angle measure cannot be
negative)