Conditional Statements
Postulates and Diagrams
Algebraic Reasoning
Properties of Equality
100
What is the hypothesis of the statement?
If it is October, then it is cold.
It is October
100
Which postulate says that
A line contains at least two points ?
line-point postulate
100
What is always the first reason in justifying the steps of algebra?
Given
100
Which property of equality is shown?
x = x
reflective POE
200
What is the conclusion of the statement?
If a quadrilateral has four equal sides, then it is a square.
It is a square
200
Which postulate justifies from the diagram that if there is a plane M, then there are three non-collinear points, D, H, F ?
Plane-Point Postulate
200
Which property is shown?
4(x+2) = 4x + 8
Distributive Property
200
Which property of equality is shown?
If a = 2 and b = 2, then a = b
transitive POE
300
What is the converse of the conditional statement?
If a polygon has 3 sides, then the polygon is a triangle.
If a polygon is a triangle, then the polygon has 3 sides.
300
Give an example of the three-point postulate from the diagram.
Answers may vary.
Must name three points first, then give the plane.
300
What property of equality justifies step 1 to step 2?
Step 1: 5x + 2 = 9x
Step 2: 2 = 4x
Subtraction POE
300
What should go in the blank to make the equation the symmetric property?
If a = b, then ______________.
b = a
400
All definitions can be written as ______________?
biconditionals (if and only if)
400
Give an example of the Line-Intersection Postulate from the diagram.
Line CH and Line GE intersect at Point D.
400
What is the next step in algebra to solve for x?
What would be the reason?
9x = 45
divide each side by 9.
division POE
400
Use the substitution property of equality to finish the sentence.
If x = 5, then x - 5 = ______.
5 - 5 = 0.
500
Can a biconditional be written given the hypothesis and conclusion?
hypothesis: It is October
conclusion: It is cold
No.
The conditional and converse are not BOTH true.
500
Give an example of the Plane-Line Postulate from the diagram.
Answers may vary.
Must first name two points on the plane, then the name of the line.
500
What is the next step in algebra to solve for x?
What would be the reason?
2x + 7 = 9x
subtract 2x from both sides.
subtraction POE
500
Give an example of the transitive property of equality.
answers may vary.