WorksheetsPractice Work: Geometry Lessons 2.1 - 2.3
Total questions: 55
Worksheet time: 52mins
Which counterexample shows that the following conjecture is false: “If angle 1 and angle 2 are supplementary, then one of the angles is obtuse”?
angle 1 = 45° and angle 2 = 45°
angle 1 = 53° and angle 2 = 127°
angle 1 = 90° and angle 2 = 90°
angle 1 = 100° and angle 2 = 80°
Which conjecture is true?
An even number plus 3 is always even.
An even number plus 3 is always prime.
An even number plus 3 is always odd.
A prime number plus 3 is always even
What is the converse of the conditional statement “If it is January, then it is winter in the United States,” ?
If it is winter in the United States, then it is January.
If it is not winter in the United States, then it is not January.
If it is not winter in the United States, then it is not January.
Not here
What is the inverse of the conditional statement “If a number is divisible by 6, then it is divisible by 3”?
If a number is divisible by 3, then it is divisible by 6.
If a number is not divisible by 6, then it is not divisible by 3
If a number is not divisible by 3, then it is not divisible by 6.
If a number is not divisible by 6, then it is divisible by 3.
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?
One of the other two angles is 90°.
One of the other two angles is obtuse.
All three angles are acute.
No conclusion can be drawn.
Which symbolic statement represents the Law of Syllogism?
If p ---> q and q ---> r are true statements, then p ---> r is a true statement.
If p ---> q and p ---> r are true statements, then q ---> r is a true statement.
If p ---> q and r ---> q are true statements, then q ---> p is a true statement.
If p ---> r and q ® r are true statements, then p ---> q is a true statement.
Which is a biconditional statement of the conditional statement “If x3 = -1, then x = -1”?
If x = -1, then x3 = -1.
x3 = -1 if x = -1.
x3 = -1 if and only if x = -1.
x = -1 ---> x3 = -1.
Find the next 2 numbers in the pattern.
1, 2, 3, 5, 8, 13, . . .
15, 20
20, 33
21, 33
21, 34
Show that the conjecture is false by finding a counterexample. The difference of two odd numbers is a prime number.
23 - 3 = 20
35 - 33 = 2
57 - 50 = 7
48 - 17 = 31
Identify the hypothesis of the statement “If an angle has a
measure less than 90°, then the angle is acute.”
If an angle has a
measure less than 90°
an angle has a
measure less than 90°
then the angle is acute
the angle is acute
Identify the conclusion of the statement “If an angle has a measure less than 90°, then the angle is acute.”
If an angle has a measure less than 90°
an angle has a measure less than 90°
then the angle is acute
the angle is acute
If a number is a prime number, then it is an odd number.
True
False
What is the inverse of the conditional statement “If the sum of two whole numbers is even, then both addends are even.”?
If the sum of two whole numbers is even, then both addends
are even.
If both addends are even, then the sum of two whole numbers is even.
If the sum of two whole numbers is not even, then both addends are not even.
If both addends are not even, then the sum of two whole numbers is not even.
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.
Valid
Not valid
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.
Valid
Not valid
A square is a rectangle with four congruent sides. Write the definition as a biconditional.
A square is a rectangle with four congruent sides.
A rectangle is a quadrilateral.
A square is a rectangle if and only if it has four congruent sides.
A square is a quadrilateral.
What is the truth value of a conditional statement "p is true, q is false'?
True
False
cannot be determined
What is the truth value of a conditional statement "p is false, q is true" ?
True
False
cannot be determined
A statement that contains the phrase "if and only if"
conditional
converse
inverse
contrapositive
biconditional
If two lines intersect to form a right angle, then they are _________.
complementary angles
parallel lines
perpendicular lines
straight lines
What is the converse statement of "If you cheat in the test, then you get a zero." ?
If you cheat in the test, then you get a zero.
If you get a zero, then you cheat in the test.
If you do not cheat in the test, then you do not get a zero.
If you do not get a zero , then you do not cheat in the test.
What is the inverse of " if p, then q." ?
If p, then q.
If not p, then not q.
If q, then p.
If not q, then not p.
Write the if-then form in conditional statement.
Two planes intersect at a line.
If two planes intersect, then their intersection is a line.
If two planes do not intersect, then their intersection is not a line.
If two planes do not intersect in a line, then they are not intersecting planes.
If two planes intersect , then their intersection is a point.
The sum of three odd integers ....
is positive integer
is negative integer
is an even integer
is an odd integer
Inductive Reasoning means...
Guessing
Using patterns to make conjectures
Explaining why
Using facts to make generalizations
Since all humans are mortal, and I am human, then I am mortal.
What type of reasoning is this?
Deductive
Inductive
All bears are mammals, all mammals have kidneys; therefore all bears have kidneys.
What type of reasoning is this?
Deductive
Inductive
What are the next 3 numbers in the pattern?
320, -160, 80, -40...
20, -10, 5
20, 10, 5
-20, -10, -5
20, 10, 0
The sum of two negative numbers is ___________.
If an animal is furry, then it is a hamster. What would be an appropriate counterexample?
goldfish
frog
elephant
cat
Identify the conclusion of the conditional statement:
If you give me twenty dollars, then I will be your best friend.
Conclusion: then I will be your friend
Conclusion: I will be your best friend
Conclusion: you give me twenty dollars
Conclusion: if you give me twenty dollars
What is this statement called: If it rains today, then we will not have practice.
If you go fishing, then you will need to bring your fishing rod.
You go fishing.
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
What statement is this symbols?
Conditional Statement
Converse
Inverse
Contrapositive
What statement is this symbols?
Conditional Statement
Inverse Statement
Converse Statement
Contrapositive Statement
What statement is this symbols?
Conditional Statement
Inverse
Converse
THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!
To write the converse you negate both the hypothesis and the conclusion of the conditional statement.
False
True
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.
Converse
Inverse
Contrapositive
Negation
When taking the inverse we _____________ the hypothesis and conclusion of the conditional statement.
negate
switch
switch and negate
leave the same
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...
__________________________ uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.
Deductive Reasoning
Inductive Reasoning
Since all humans are mortal, and I am human, then I am mortal.
What type of reasoning is this?
Deductive
Inductive
All chickens that we have seen have been brown; so, all chickens are brown.
What type of reasoning is this?
Deductive
Inductive
ALWAYS, SOMETIMES or NEVER:
Through any two points, there exists exactly one line.
Always
Sometimes
Never
Which of the following cannot be assumed from the diagram?
Points A, B, C and E are coplanar
Points F, B and G are colinear
Line EC intersects plane M at point C
