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Practice Work: Geometry Lessons 2.1 - 2.3

Total questions: 55

Worksheet time: 52mins

Name
Class
Date
1.

Which counterexample shows that the following conjecture is false: “If angle 1 and angle 2 are supplementary, then one of the angles is obtuse”?

a)

angle 1 = 45° and angle 2 = 45°

b)

angle 1 = 53° and angle 2 = 127°

c)

angle 1 = 90° and angle 2 = 90°

d)

angle 1 = 100° and angle 2 = 80°

2.

Which conjecture is true?

a)

An even number plus 3 is always even.

b)

An even number plus 3 is always prime.

c)

An even number plus 3 is always odd.

d)

A prime number plus 3 is always even

3.

What is the converse of the conditional statement “If it is January, then it is winter in the United States,” ?

a)

If it is winter in the United States, then it is January.

b)

If it is not winter in the United States, then it is not January.

c)

If it is not winter in the United States, then it is not January.

d)

Not here

4.

What is the inverse of the conditional statement “If a number is divisible by 6, then it is divisible by 3”?

a)

If a number is divisible by 3, then it is divisible by 6.

b)

If a number is not divisible by 6, then it is not divisible by 3

c)

If a number is not divisible by 3, then it is not divisible by 6.

d)

If a number is not divisible by 6, then it is divisible by 3.

5.

Given: If one angle of a triangle is a right angle, then the other two angles are both acute. A triangle has a 45 angle.

What conclusion can be drawn?

a)

One of the other two angles is 90°.

b)

One of the other two angles is obtuse.

c)

All three angles are acute.

d)

No conclusion can be drawn.

6.

Which symbolic statement represents the Law of Syllogism?

a)

If p ---> q and q ---> r are true statements, then p ---> r is a true statement.

b)

If p ---> q and p ---> r are true statements, then q ---> r is a true statement.

c)

If p ---> q and r ---> q are true statements, then q ---> p is a true statement.

d)

If p ---> r and q ® r are true statements, then p ---> q is a true statement.

7.

Which is a biconditional statement of the conditional statement “If x3 = -1, then x = -1”?

a)

If x = -1, then x3 = -1.

b)

x3 = -1 if x = -1.

c)

x3 = -1 if and only if x = -1.

d)

x = -1 ---> x3 = -1.

8.

Find the next 2 numbers in the pattern.

1, 2, 3, 5, 8, 13, . . .

a)

15, 20

b)

20, 33

c)

21, 33

d)

21, 34

9.

Show that the conjecture is false by finding a counterexample. The difference of two odd numbers is a prime number.

a)

23 - 3 = 20

b)

35 - 33 = 2

c)

57 - 50 = 7

d)

48 - 17 = 31

10.

Identify the hypothesis of the statement “If an angle has a

measure less than 90°, then the angle is acute.”

a)

If an angle has a

measure less than 90°

b)

an angle has a

measure less than 90°

c)

then the angle is acute

d)

the angle is acute

11.

Identify the conclusion of the statement “If an angle has a measure less than 90°, then the angle is acute.”

a)

If an angle has a measure less than 90°

b)

an angle has a measure less than 90°

c)

then the angle is acute

d)

the angle is acute

12.

If a number is a prime number, then it is an odd number.

a)

True

b)

False

13.

What is the inverse of the conditional statement “If the sum of two whole numbers is even, then both addends are even.”?

a)

If the sum of two whole numbers is even, then both addends

are even.

b)

If both addends are even, then the sum of two whole numbers is even.

c)

If the sum of two whole numbers is not even, then both addends are not even.

d)

If both addends are not even, then the sum of two whole numbers is not even.

14.

Given: If a ray bisects an angle, two congruent angles are formed.

ray YW bisects angle XYZ.

Conjecture: angle XYW is congruent to angle WYZ

Determine whether the conjecture is valid by the Law of Detachment.

a)

Valid

b)

Not valid

15.

Given: If a number is a prime number, then it is an odd number. If a number is not divisible by 2, then it is an odd number. Conjecture: If a number is not divisible by 2, then it is a prime number. Determine whether the conjecture is valid by the Law of Syllogism.

a)

Valid

b)

Not valid

16.

A square is a rectangle with four congruent sides. Write the definition as a biconditional.

a)

A square is a rectangle with four congruent sides.

b)

A rectangle is a quadrilateral.

c)

A square is a rectangle if and only if it has four congruent sides.

d)

A square is a quadrilateral.

17.

What is the truth value of a conditional statement "p is true, q is false'?

a)

True

b)

False

c)

cannot be determined

18.

What is the truth value of a conditional statement "p is false, q is true" ?

a)

True

b)

False

c)

cannot be determined

19.

A statement that contains the phrase "if and only if"

a)

conditional

b)

converse

c)

inverse

d)

contrapositive

e)

biconditional

20.

If two lines intersect to form a right angle, then they are _________.

a)

complementary angles

b)

parallel lines

c)

perpendicular lines

d)

straight lines

21.

What is the converse statement of "If you cheat in the test, then you get a zero." ?

a)

If you cheat in the test, then you get a zero.

b)

If you get a zero, then you cheat in the test.

c)

If you do not cheat in the test, then you do not get a zero.

d)

If you do not get a zero , then you do not cheat in the test.

22.

What is the inverse of " if p, then q." ?

a)

If p, then q.

b)

If not p, then not q.

c)

If q, then p.

d)

If not q, then not p.

23.

Write the if-then form in conditional statement.

Two planes intersect at a line.

a)

If two planes intersect, then their intersection is a line.

b)

If two planes do not intersect, then their intersection is not a line.

c)

If two planes do not intersect in a line, then they are not intersecting planes.

d)

If two planes intersect , then their intersection is a point.

24.

The sum of three odd integers ....

a)

is positive integer

b)

is negative integer

c)

is an even integer

d)

is an odd integer

25.

Inductive Reasoning means...

a)

Guessing

b)

Using patterns to make conjectures

c)

Explaining why

d)

Using facts to make generalizations

26.

Since all humans are mortal, and I am human, then I am mortal.

What type of reasoning is this?

a)

Deductive

b)

Inductive

27.

All bears are mammals, all mammals have kidneys; therefore all bears have kidneys.

What type of reasoning is this?

a)

Deductive

b)

Inductive

28.
Given, "If I have a Siberian Husky, then I have a dog." Identify the hypothesis.
a)
If I have a Siberian Husky.
b)
I have a Siberian Husky.
c)
Then I have a dog.
d)
I have a dog.
29.

What are the next 3 numbers in the pattern?

320, -160, 80, -40...

a)

20, -10, 5

b)

20, 10, 5

c)

-20, -10, -5

d)

20, 10, 0

30.
How can you prove a conjecture is false?
a)
Counterexample
b)
Not Possible
c)
Patterns
31.
Complete the conjecture.
The sum of two negative numbers is ___________.
a)
positive
b)
negative
c)
odd
d)
even
32.

If an animal is furry, then it is a hamster. What would be an appropriate counterexample?

a)

goldfish

b)

frog

c)

elephant

d)

cat

33.

Identify the conclusion of the conditional statement:


If you give me twenty dollars, then I will be your best friend.

a)

Conclusion: then I will be your friend

b)

Conclusion: I will be your best friend

c)

Conclusion: you give me twenty dollars

d)

Conclusion: if you give me twenty dollars

34.
Given, "If angles are congruent, then the measures of the angles are equal." Identify the contrapositive.
a)
If the measures of the angles are equal, then the angles are congruent.
b)
If angles are not congruent, then the measures of the angles are not equal.
c)
If the measures of the angles are not equal, then the angles are not congruent.
d)
If the angles are not congruent, then the measure of the angles are equal.
35.
Conditional: If it does not rain today, then we will have practice.
What is this statement called: If it rains today, then we will not have practice.
a)
Converse
b)
Inverse
c)
Contrapositive
d)
Negation
36.
Given, "If angles are congruent, then the measures of the angles are equal." Identify the conclusion.
a)
If the angles are congruent.
b)
The angles are congruent.
c)
Then the measures of the angles are equal.
d)
The measures of the angles are equal.
37.
Used to prove that a conjecture is false.
a)
Counterexample
b)
Inductive Reasoning
c)
Concluding statement
d)
Conjecture
38.
Draw a conclusion from the statement.
If you go fishing, then you will need to bring your fishing rod.
You go fishing.
a)
You will need to bring your fishing rod.
b)
Invalid
c)
You are a boring person.
d)
You are going to catch a fish.
39.
Use the law of syllogism to draw a conclusion from the two given statements:
Statement 1: If you exercise regularly, then you have a healthy body
Statement 2: If you have a healthy body, then you have more energy
a)
You have more energy
b)
If you exercise regularly, then you have more energy
c)
You have a healthy body
d)
If you do not have a healthy body, then you do not exercise regularly
40.

What statement is this symbols?

a)

Conditional Statement

b)

Converse

c)

Inverse

d)

Contrapositive

41.
What is the inverse to this statement?
a)
If you live in Canada, you live in Montreal
b)
If you don't live in Montreal, then you don't live in Canada.
c)
If you don't live in Canada, you don't live in Montreal.
d)
Montreal is in Brazil.
42.

What statement is this symbols?

a)

Conditional Statement

b)

Inverse Statement

c)

Converse Statement

d)

Contrapositive Statement

43.

What statement is this symbols?

a)

Conditional Statement

b)

Inverse

c)

Converse

d)

THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!

44.

To write the converse you negate both the hypothesis and the conclusion of the conditional statement.

a)

False

b)

True

45.

Conditional: If Elsa gets married, then the reception will be at the country club.

What is this statement: If the reception is at the country club, then Elsa will be getting married.

a)

Converse

b)

Inverse

c)

Contrapositive

d)

Negation

46.
What is the hypothesis of the given Conditional Statement?
a)
Jimmy will go to Orlando
b)
Jimmy goes on vacation
c)
Jimmy will go to Orlando
d)
Who is Jimmy?
47.

When taking the inverse we _____________ the hypothesis and conclusion of the conditional statement.

a)

negate

b)

switch

c)

switch and negate

d)

leave the same

48.
What is the conclusion of the following statement: "The angles are supplementary, if they add up to 180 degrees."
a)
if they add up to 180 degrees
b)
the angles are supplementary
c)
they add up to 180 degrees
d)
there is no conclusion
49.
Inductive Reasoning means...
a)
Guessing
b)
Testing and observing patterns to make conjectures
c)
Explaining why
d)
Ura nok seblu!
50.
Using deductive reasoning, which of the following completes the statement to form a valid conclusion?
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily, then...
a)
Look out for the snowplows while driving to school.
b)
The big test will not be given today.
c)
The roads will be hard to drive on.
d)
You should call the school to see if school is canceled.
51.

__________________________ uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.

a)

Deductive Reasoning

b)

Inductive Reasoning

52.

Since all humans are mortal, and I am human, then I am mortal.

What type of reasoning is this?

a)

Deductive

b)

Inductive

53.

All chickens that we have seen have been brown; so, all chickens are brown.

What type of reasoning is this?

a)

Deductive

b)

Inductive

54.

ALWAYS, SOMETIMES or NEVER:

Through any two points, there exists exactly one line.

a)

Always

b)

Sometimes

c)

Never

55.

Which of the following cannot be assumed from the diagram?

a)

Points A, B, C and E are coplanar

b)

Points F, B and G are colinear

c)
d)

Line EC intersects plane M at point C