Angles & Angle Relationships
Identify and Label Points, Lines, Rays & Planes
Symbolic logic; converse, inverse, contrapositive, biconditional
Deductive reasoning and Venn diagrams
Riddles
Disney Characters
Fast Food Items
100
Two angles whose measures add up to 90° are called ___ angles.
Complementary angles
100
How many points determine exactly one line?
Two points
100
Identify the hypothesis: “If it rains, then the game is canceled.”
It rains
The hypothesis (p) follows “if”; the conclusion (q) follows “then.”
100
A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. Find A ∩ B
{3, 4}
Intersection (∩) means the elements in both sets
100
What has a face and two hands, but no arms or legs?
A clock
100
In Frozen, what is the name of the snowman who loves warm hugs?
Olaf
100
The Big Mac is the signature burger of which restaurant chain?
McDonald’s
200
∠1 and ∠2 form a linear pair. If m∠1 = 68°, what is m∠2?
112°
A linear pair is supplementary: 180 − 68 = 112
200
Name the figure written with the symbol shown.
Ray PQ
Its endpoint is P, and it extends forever through Q. The first letter is always the endpoint.
200
Let p: “The angle is acute.” Let q: “The angle measures 40°.” Write q ∧ ~p in words.
The angle measures 40° and the angle is not acute.
∧ means “and,” ~ means “not.” (This compound statement is false — a 40° angle is acute.)
200
Given: If a student earns an A, then the student makes the honor roll. Maria earns an A. What can you conclude, and which law did you use?
Maria makes the honor roll — Law of Detachment
200
What gets wetter the more it dries?
A towel
200
In The Lion King, who is Simba’s father?
Mufasa
200
“Have it your way” — the Whopper is sold at which chain?
Burger King
300
The two vertical angles shown are labeled with expressions. Find x.
x = 20
Vertical angles are congruent: 3x + 10 = 5x − 30, so 40 = 2x. Each angle measures 70°
300
Two distinct planes intersect. What is their intersection?
A line
300
Write the converse of “If two angles are vertical angles, then they are congruent.” Is the converse true?
If two angles are congruent, then they are vertical angles. False.
Counterexample: the base angles of an isosceles triangle are congruent but are not vertical angles
300
The Venn diagram shows a class of 30 students. How many students play neither sports nor band?
5 students
13 + 5 + 7 = 25 are inside the circles, so 30 − 25 = 5 are outside both.
300
I am an odd number. Take away one letter and I become even. What number am I?
Seven
Remove the S and you get “even.”
300
In Moana, which shapeshifting demigod helps Moana restore the heart of Te Fiti?
Maui
300
The Frosty is the famous dessert at which chain?
Wendy’s
400
Two parallel lines are cut by a transversal. Alternate interior angles measure (4x + 6)° and (6x − 24)°. Find the measure of each angle.
66°
Alternate interior angles are congruent: 4x + 6 = 6x − 24, so x = 15 and 4(15) + 6 = 66.
400
Two lines are not coplanar and never intersect. What are they called?
Skew lines
Parallel lines never intersect either, but parallel lines are coplanar. In the figure, lines ℓ and m are skew.
400
Write the contrapositive of “If a figure is a square, then it has four sides,” and give its symbolic form.
If a figure does not have four sides, then it is not a square. ~q → ~p
A conditional and its contrapositive are logically equivalent, so both are true.
400
Given: If a polygon is a square, then it is a rectangle. If a polygon is a rectangle, then it is a parallelogram. What conclusion follows, and which law was used?
If a polygon is a square, then it is a parallelogram — Law of Syllogism
400
What has keys but can’t open a single lock?
A piano (or a keyboard)
400
In Aladdin, what is the name of Jafar’s wisecracking parrot?
Iago
400
The Crunchwrap Supreme is a menu item at which chain?
Taco Bell
500
The supplement of an angle is 12° more than three times its complement. Find the angle.
51°
180 − x = 3(90 − x) + 12 → 180 − x = 282 − 3x → 2x = 102. Check: supplement 129°, complement 39°, and 3(39) + 12 = 129
500
Points A, B, and C are collinear. How many different planes contain all three points?
Infinitely many
Any plane that contains line AC works, which is why a plane is determined by three noncollinear points
500
“If an angle is a right angle, then it measures 90°.” Can this be written as a true biconditional? If so, write it in words and in symbols.
Yes: An angle is a right angle if and only if it measures 90°. p ↔ q
A biconditional is true when both the conditional and its converse are true.
500
Given: If an angle is acute, then it measures less than 90°. m∠B = 120°. What can you conclude, and which law did you use?
∠B is not acute — Law of Contrapositive
The conclusion is false (∠B is not less than 90°), so the hypothesis must be false.
500
A man pushes his car up to a hotel and immediately tells the owner he’s bankrupt. Why?
He’s playing Monopoly
500
In Tangled, what is the name of the palace horse who chases Flynn Rider?
Maximus
500
Ordering your burger “Animal Style” is a not-so-secret menu option at which West Coast chain?
In-N-Out Burger