Vocabulary
What is the proper name of an "if-then" statement?
A conditional statement
How do you negate the statement:
"Today is Friday"
Today is NOT Friday.
What two numbers come next in this pattern and why?
1, 3, 5, 7, 9, 11, .....
13, 15 - they are odd numbers.
Use the law of detachment to make a conclusion:
If you do your homework, then you can go to the movies. You finished your homework today...
You can go to the movies.
When you add the same number to both sides of an equation.
Addition Property of Equality
What kind of angles are across from each other and have the same measure?
Vertical Angles
What is the inverse of this statement:
"If you are in New York City, then you are in the united States."
If you are NOT in New York City, then you are NOT in the United States.
Use Inductive Reasoning to make a Conclusion
Each time you brother goes to the store, he buys milk. So, the next time he goes to the store, he will...
buy milk.
Valid or Invalid?
If it is raining, then practice will be cancelled. If practice is cancelled, then you can go to the mall after school. Therefore if it is raining, then you can go to the mall after school today.
VALID - law of syllogism
The act of replacing something with a different value.
Substitution
What phrase is used in a biconditional statement?
"if and only if"
What is the converse of this statement:
"If the stars are visible, then it is night."
If it is night, then the stars are visible.
Make a conjecture about the product of an even number and an odd number.
The product will be even.
3(4)=12 7(2) = 14 5(6) = 30
Use the law of syllogism to create a new conditional statement.
If you stay up late, then you will be tired in the morning. If you are tired in the morning, then you will do bad on your test.
If you stay up late, then you will do bad on your test.
What step always begins a proof?
The "Given"
What do we call an unproven statement based on observations?
Conjecture
What is the contrapositive of this statement:
"If you do your homework, then you will do well on the test."
If you do NOT do well on the test, then you did NOT do your homework.
Use Deductive Reasoning to make a conclusion
All reptiles are cold-blooded. Parrots are not cold-blooded. That means parrots are...
not reptiles.
Valid or Invalid?
If you pass the final, then you will pass the class. You passed the class. Therefore you must have passed the final.
INVALID - you could have passed the class without passing the final...wrong order for law of detachment
What property is this an example of:
If segment AB is equal to segment CD, and segment CD is 10 inches, then segment AB must also be 10 inches.
Transitive Property
A specific case for which a conjecture is false.
Counterexample
Write this definition as a biconditional:
"Two angles are supplementary angles when the sum of their measures is 180 degrees."
Two angles are supplementary angles if and only if the sum of their measures is 180 degrees.
Give me a counter example to the statement:
If two angles are supplements to each other, then one of them must be an obtuse angle.
You could have two right angles, then neither of them is obtuse.
Using the law of detachment, what conclusion can be reached from the following:
If you are on the basketball team, then you have practice on Thursday. You have practice on Thursday...
No conclusion can be made. We don't know if the hypothesis is true...
What two things does the Linear Pair Postulate tell us?
Two angles are supplementary and they add up to 180 degrees.