Algebraic proofs

Segment proofs

Conditional statements

Logic

Math related trivia

100

If a=b, then a+c = b+c

Addition Property

100

If M is the midpoint of AB,

then AM=MB

Definition of a midpoint

100

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.

100

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

100

What time is it?

4:45

200

If a = b, then a * c = b* c

Multiplication property

200

If AB=DE, then DE=AB

Symmetric Property

200

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.

200

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

200

What is the only even prime number?

2

300

a(b+c) = ab + ac

Distributive property

300

If UV is congruent to GH, then UV=GH

Definition of congruence

300

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.

300

T/F. Provide a counter example if false.

Squaring a number and adding three will always result in an even number.

False.

Ex. 2^{2 }

300

What number is twice the sum of its digits?

18

400

If k = m and m = n, then k = n

Transitive property

400

If IC + ES = PI, and CE = ES, then IC + CE = PI

Substitution property

400

Original statement:

If the power strip is on, then your computer has power.

What is the **biconditional **statement here?

Your power strip is on **if and only if **your computer has power.

400

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!

1.25, 0.625, 0.3125

(5/4, 5/8, 5/16)

400

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.

500

For any real number a, a=a

Reflexive propert

500

If ST is congruent to AR and AR is congruent to BU, then ST is congruent to BU

Transitive property

500

What kind of statement is this?

The muffins are burnt or the muffins are undercooked.

A disjunction! (p **or** q)

500

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

500

In a group of 23 people, what is the probability that two will share the same birthday?

50%

This is called the **birthday paradox**