Patterns and Reasoning Conditional Statements Related Conditional Statements Biconditional Statements Deductive Reasoning
81 and 243
What are the next two terms in 3, 9, 27, ...?
An angle measures 130
What is the hypothesis of the statement
"If an angle measures 130, then the angle is obtuse"
False
What is the truth value of "If A = 140º, then A is acute"
No. Not reversible, Dolphins, Turtles, Whales also swim.
Is this a good definition?
"A fish is an animal that swims"
Rachel will pass the course.
What can you conclude from the statement
"If a students gets an A on the final exam, then the student will pass the course.
Rachel got an A on her history final exam."
1/10 and 1/100 or 0.1 and 0.01
What are the next two terms in 100, 10, 1, ...
They share a vertex
What is the conclusion of the statement
"If two angles are vertical, then they share a vertex"
If a is not acute (Add not)
What is the negation of "If A is acute"
Yes. If an angle is a straight angle, then it measures 180º
Is the following statement reversible?
"If an angle measures 180º, then it is a straight angle"
No conclusion.
What can you conclude from the statement
"If two angles are adjacent, then they share a common vertex.
Angles 1 and 2 share a common vertex."
1/16 and 1/32
What are the next two terms in 1/2, 1/4, 1/8, ...
If an animal is a dolphin, then it is a mammal.
How can you write "Dolphins are mammals" as a conditional statement?
If A is acute, then A = 14º (Switch order)
What is the converse of "If A = 14º, then A is acute"
If and only if
What four words are in a biconditional statement?
If a figure is a square, then it has four sides.
What can you conclude from the statement
"If a figure is a square, then the figure is a rectangle.
If a figure is a rectangle, then it has four sides."
January
What is a counterexample for the statement
"If the name of a month starts with the letter J, it is a summer month."
False. Example: 6/3=2 and 6 is even.
Is this conditional true or false?
"If a number is divisible by 3, then it is odd"
If A ≠ 14º, then A is not acute (Add not)
What is the inverse of "If A = 14º, then A is acute"
The conditional and the converse
Which 2 related conditionals need to be true for a biconditional statement?
Conditional, Converse, Inverse, Contrapositive
No conclusion.
What can you conclude from the statement
"If you do gymnastics, then you are flexible.
If you do ballet, then you are flexible."
Any negative number. Ex: -2 x 2 = -4, -4 < -2
What is a counterexample for the statement
"When you multiply a number by 2, the product is greater than the original number."
True
Is this conditional true or false?
"If two angles form a linear pair, then they are supplementary"
If A is not acute, then A ≠ 14 (Add not and switch order)
What is the contrapositive of "If A = 14º, then A is acute"
A polygon has four sides if and only if it is a quadrilateral
Write the statement as a biconditional.
"If a polygon has four sides, then it is a quadrilateral."
Law of Detachment and Law of Syllogism
What is the name of the laws used to make conclusions from statements? (Need 1 of the 2 answers)