Statements
Truth Tables
Laws and Postulates
Properties
Solve
100
Write the statement in if-then form.
An acute angle measures less than 90.
If an angle is acute, then it measures less than 90.
100
Which would be the values in the not p column?
F
F
T
T
100
Which is a type of proof where you write a paragraph to explain why a conjecture for a given situation is true?
Paragraph Proof
100
What property justifies the statement?
If 3(x - 4) = 2x + 7, then 3x - 12 = 2x + 7.
Distribution
100
Find the value of x.
Vertical Angle Theorem states that if two angles are vertical angles, then they are congruent.
x = 25
200
Make a Conjecture about the next term in the sequence: 92,87,82,77,72
The number is 5 less than the previous.
67
200
Which would be the values in the not p or q column?
T
F
T
T
200
Which Law does the following illustration depict?
[(p->q) and p]->q
Law of Detachment
200
What property justifies the statement?
If 3x = 6, then x = 2.
Division
200
If the measure of angle ABD = 56, find the measure of angle DBC.
Complementary Angles add up to 90 degrees,
so angle DBC = 34 degrees
300
Make a conjecture given that M is the midpoint of segment BC.
Midpoint Theorem state if M is the midpoint of segment BC, then Segment BM is congruent to Segment MC.
BM = MC
300
Identify the hypothesis of the statement If x + 4 = 5, then x = 1.
Hypothesis is the statement that would be given, or the statement following the word If.
H: x + 4 = 5
300
Which Law does the following illustration depict?
[(p->q) and (q->r)]->(p->r)
Law of Syllogism
300
What property justifies the statement?
If measure of angle A = 10 and measure of angle B = 10, then measure of angle A = measure of angle B.
Substitution
300
If a right angle is trisected, what is the measure of each of the smaller angles?
Trisected means to break into three even segments, so the measure of each angle would be
400
What is the counterexample for:
If a + b <= 8 and a = 2, then b <= 5.
Counterexample means a false example, to make your conjecture not true.
b = 6
400
Identify the converse of the statement If cats fly, then ducks bark.
Converse means flipping the If and Then statement around.
If ducks bark, then cats fly
400
Determine whether each statement is always, sometimes, or never true. Explain.
If two angles are complementary, then they form a right angle.
Sometimes; if the angles are adjacent, they will form a right angle, but if they are not adjacent, they will not.
400
What property justifies the statement?
if segment PS is congruent to segment WX, then PS = WX.
Definition of Congruent Segments
400
If the measure of angle 1 is twice the measure of angle 2, find measure of angle 1.
The picture shows a straight line, so the total degrees if you add up both angles would be 180.
M1 = 2*M2 -> M1 + M2 = 180 -> 2*M2 + M2 = 180 -> 3*M2 = 180 -> M2 = 60
M1 = 2*(60) = 120 degrees
500
If p is true and q is false, what is the truth value of p or q?
True
500
Identify the inverse of the statement If a triangle has 3 equal sides, then it is equilateral.
Inverse means the negating the If and Then statements.
If a triangle does not have 3 equal sides, then it is not equilateral.
500
What best describes the statement A plane contains at least 3 points not on the same line?
Always True, because postulate 2.4 states a plane contains at least three noncolinear points.
500
If A, B, and N are collinear and AB + BN = AN, which point is between the other two points?
Point B, because Postulate 2.9 states that If A, B, N are collinear then point B is between A and C if and only if AB + BN = AN.
500
Find the measure of each numbered angle, and name the theorems that justify your work.
7 = 81, 8 = 99, Supplement Theorem.
5 = 81, 6 = 99, Vertical Angles Theorem.