Properties
Conditional Variants
Postulates & Theorems
Solve the Problem
100
If 4x=24
then x=6
Division Property of Equality
100
What is the contrapositive statement of'
"If a figure has four sides, then it is a square."
"If a figure is not a square, then it does not have four sides."
100
If point B is on line segment AC,
then AB + BC = AC
Segment Addition Postulate
100
You have a pair of vertical angles. The first measures (x+10). The second measure (4x-35). What is the value of x?
x=15
200
If angle A is congruent to angle C
and angle C is congruent to angle F,
then angle A is congruent to angle F.
Transitive Property of Equality
200
What is the truth value of the INVERSE of this statement?
"If 2x=12, then x is greater than 5."
False
200
True or False:
The Definition of Congruency says that congruent angles have equal measures.
True
200
Two angles are supplementary. The first is 76 degrees. The second is 2x-4. What is the value of x?
x=40
300
If a=-4
then 6a+2 = 6(-4)+2
Substitution Property
300
What is the biconditional statement of this conditional statement?
"If a rectangle has four congruent sides, then it is a square."
"A rectangle is a square if and only if it has four congruent sides."
300
If two angles are congruent AND supplementary, then each angle is ___________.
a right angle (90 degrees)
300
Y is a point collinear with and between X and Z. If XY=42 and YZ=20, what is the value of XZ?
62
400
If PR = QS and PQ + QR = PR
then QS = PQ + QR
Transitive Property of Equality
(or Substitution Property)
400
Use the Law of Syllogism to write a conclusion
If it snows on Monday, school will be canceled.
If school is canceled, Mrs. Case is going to the Bahamas.
If it snows on Monday, Mrs. Case is going to the Bahamas.
400
What theorem is used here?
If two angles form a linear pair, then they are supplementary.
Linear Pair Theorem
(aka Supplement Theorem)
400
Given: 10 = 2x - 6
What FOUR reasons will be needed in a two-column proof to prove that x=8?
Given
Addition Property of Equality
Division Property of Equality
Symmetric Property
500
3(x-4) = 3x - 12
Distributive Property
500
Use the Law of Detachment to write a conclusion:
If we all get A's on the test, Mrs. Ward will give us an ice cream party.
We all get A's on the test.
Mrs. Ward is giving us an ice cream party!
500
What Theorem is used here?
If two angles are supplementary to the same angle, then those two angles are congruent.
Congruent Supplements Theorem
500
Draw a diagram in which the Angle Addition Postulate shows that the measure of angle BAC + the measure of angle CAD = the measure of angle BAD.
