Twisted Logic
Theorems, Postulates & Such
I ❤️ Algebra I (ft. the Wheel)
So you think you know Mr. Dutelle?
Induction!
Reason-maxxing
emerge mo tryst
Just spin The Wheel, bruh
1
Given: "If it is sunny, then we go to the park"
"If we go to the park, then we eat ice cream."
What conditional can be written and, what Law would be used?
"If it is sunny, then we eat ice cream."
Law of Syllogism!
1
What is the difference between a postulate and a theorem?
A postulate is an accepted statement of fact whereas a theorem must be proven true using logical reasoning, definitions & postulates.
1
Factor!
6x^2-x-2
(2x+1)(3x-2)
1
You have all seen pictures of Mr Dutelle's dog, Savannah. She was flown to him from a rescue shelter from what state?
Texas
1
Which is the odd ball out??? (And Why????)
119 - The others have digits that add to 7!
1
The Coal, Carrot & Scarf
Five pieces of coal, a carrot, and a scarf are lying on the lawn. Nobody put them on the lawn, but there is a perfectly logical reason for them being there. What is it?
They were used by children to make a snowman. The snow has since melted
1
Ariel in par
Linear Pair!
1
Wheel Spin #1
Wheel Spin #1
2
"If it rains heavily, the football field is muddy."
You go outside to see that the football field is muddy.
What conclusion, if any, can you draw and what Law would be used?
None
2
Finish this Postulate...
If two planes intersect, then...
"they intersect in exactly one line"
2
Simplify!
sqrt(192x^12y^9z^-4
(8x^6y^4sqrt(3y))/z^2
2
Mr. Dutelle has been at DMS for a while! How many years has it been (this includes one year as Mr. Cutone's student teacher).
20!
2
What number comes next in the sequence?
143, 120, 99, 80, 63, 48,...
35
2
The Man in the Elevator
A man lives on the tenth floor of a building. Every day, he takes the elevator to the first floor to go to work or to go shopping. When he returns, he always takes the elevator to the seventh floor and then walks the remaining flights of stairs to his apartment on the tenth floor.
Why does he do this?
The man is too short to reach all of the buttons. He can reach the button for the first floor (so he can go to work or shop), but he cannot reach the button for the tenth floor. The seventh floor button must be the highest he can reach.
2
Algol fowl missy
Law of Syllogism!
2
Wheel Spin #2
Wheel Spin #2
5
What is the symbolic form of the Law of Detachment?
5
What are the midpoint and distance formulas?
5
Find x & y!
x = 4sqrt3
y=2sqrt3
5
Mr. Dutelle doesn't coach here at DMS anymore, but he used to. Name all of the sports he used to coach here!
Basketball (boys & girls), Soccer (boys), Volleyball (girls).
Plus a few years coaching Girls' Lacrosse at the HS!
5
What is the missing number in wheel C?
8. Each side of the wheel must add to the same # as the other side. 9 + 8 = 17, which matches the left side of the wheel
5
Birthday Blues!
The day before yesterday, Pip was 17. Pip says "next year, I will be 20!"
How can this be so?
Pip made the statement on January 1st and her birthday must be on December 31st.
She was 17 the day before yesterday.
She was 18 yesterday.
This year she will be 19.
Next year she will be 20.
5
recouple taxmen
Counterexample!
5
Wheel Spin #3
Wheel Spin #3
10
State the contrapositive of this conditional.
"If it is my birthday, then I will eat cookie cake."
"If I don't eat cookie cake, then it's not my birthday."
10
Name this Postulate/Theorem...
"If two lines & a transversal form alternate interior angles that are congruent, then the lines are parallel."
Converse of the Alternate Interior Angles Theorem
10
Simplify this radical expression!
(8x^2-36x-20)/(2x^2-50)
(2(2x+1)) / (x+5
10
Mr. Dutelle did not grow up in Pittsburgh but he did grow up in a city/town with an ACC program. Name the city or town.
Hint: The city is the one with an ACC program there. The town actually has the same name as a Premier League team!
Syracuse (NY) is the city.
Liverpool (NY) is the town.
10
What # should go at the bottom of the STAR?
189
10
Chess Masters
Two grandmasters played five games of chess. Each won the same number of games and lost the same number of games. There were no draws in any of the games.
How can this be so?
Nobody said they were playing against each other!
10
Amery planets plunges
Supplementary Angles!
10
Wheel Spin #4
Wheel Spin #4
20
Which conditionals/statements must share the same truth value?
Conditional & Contrapositive
Converse & Inverse
20
State the Congruent Supplements Theorem
"If two angles are supplements of the same angle (or congruent angles), then they are congruent to each other."
20
Simplify!
((64g^-2k^4)/(4g^-6k^6))^-2
k^4/(256g^8)
20
Mr. Dutelle's first dog was named after a character on the office. Name that dog!
DWIGHT
20
Marshall can paint a fence in 2 hours
Zoey can paint the same fence in 3 hours
Ryan can paint it in 4 hours
Lucy can paint that very same fence in 6 hours
How long would it take for them to paint the fence if they worked together?
.8 hours or 48 minutes
20
Push that Car
A man pushing his car stopped outside a hotel. As soon as he got there, he knew he was bankrupt. Why?
He was playing Monopoly!
20
dancer pulpier
Perpendicular!
20
Wheel Spin #5
Wheel Spin #5