Algebraic proofs
If a=b, then a+c = b+c
Addition Property
If M is the midpoint of AB,
then AM=MB
Definition of a midpoint
Original conditional statement:
If you eat cake, then you are eating sugar.
What is the converse?
If you are eating sugar, then you are eating cake.
T/F and provide a counter example if F.
If you are in the contiguous 48 states, then you are in the United States
True
What time is it?
4:45
If a = b, then a * c = b* c
Multiplication property
If AB=DE, then DE=AB
Symmetric Property
Original statement:
If you made a mistake, then you lose points.
What is the inverse?
If you did not make a mistake, then you did not lose points.
T/F. Provide a counter example if false.
If a state borders the ocean, then it is on the East Coast.
False.
California, OR, WA, TX, LA, AL, AK, HI
What is the only even prime number?
a(b+c) = ab + ac
Distributive property
If UV is congruent to GH, then UV=GH
Definition of congruence
Original statement:
If your car is covered in frost, then it froze last night.
What is the contrapositive statement?
If it did not freeze last night, then your car is not covered in frost.
T/F. Provide a counter example if false.
Squaring a number and adding three will always result in an even number.
False.
Ex. 22
What number is twice the sum of its digits?
18
If k = m and m = n, then k = n
Transitive property
If IC + ES = PI, and CE = ES, then IC + CE = PI
Substitution property
Original statement:
If the power strip is on, then your computer has power.
What is the biconditional statement here?
Find the next three terms of the sequence. Then, write a conjecture explaining how to find the next terms.
20, 10, 5, 2.5, _______, _______, ________
NO CALCULATOR!
(5/4, 5/8, 5/16)
What is a rational number?
A number that can be expressed as a fraction.
Pi is not a rational number, neither are square roots of non-perfect squares.
For any real number a, a=a
Reflexive propert
Transitive property
What kind of statement is this?
The muffins are burnt or the muffins are undercooked.
A disjunction! (p or q)
Find the next 3 terms in the sequence and write a conjecture that describes how to find these terms.
2, 5, 11, 23, 47, _____, ______, ______
95, 181, 383
In a group of 23 people, what is the probability that two will share the same birthday?
50%
This is called the birthday paradox