Postulates
Deductive Reasoning
Algebra Properties
Parallel Lines
Proof
100
AB + BC = AC
Segment Addition Postulate
100
Given: If p then q
p
Conclude: q
The Law of Detachment
100
If a = b, then a - c = b - c
Subtraction property
100
Name a pair of same-side interior angles.
angle 3 and angle 5
angle 4 and angle 6
100
Give a reason for this step:
3x - 4 = 23
3x = 27
Addition property
200
m angle AOB + m angle BOC = m angle AOC
Angle Addition Postulate
200
Given: If p then q
If q then r
Conclude: If p then r
Law of Syllogism
200
a(b + c)=a cdot b+a cdot c
Distributive property
200
Name a pair of alternate exterior angles.
angle 1 and angle 8
angle 2 and angle 7
200
Give a reason for this step:
AB + BC = AC
x-1 + 3x -7 = x+7
Substitution property
300
Solve for x
x=5
300
If an animal has six legs, then it's an insect.
Ants have six legs.
Ants are insects.
300
Division property
If a = b and c ne 0, then a/c = b/c
300
angle 1 and angle 7
Same-side exterior angles
300
m angle QWT + m angle TWX = 90^circ
Definition of complementary angles
400
What equation could you write from this diagram?
m angle QWT + m angle TWX = m angle QWX
2x + x +6 = 90
400
If the sum of the digits of a number is divisible by 9, then the number is divisible by 9.
If a number is divisible by 9, then it's divisible by 3.
If the sum of the digits of a number is divisible by 9, then it's divisible by 3.
400
Reflexive property
a=a
400
angle 3 and angle 7
Corresponding angles
400
2x + x + 6 = 90
3x + 6 = 90
Distributive property
500
m angle 3 + m angle 4 = 180^circ
Same-side interior angle postulate
500
If you eat yogurt, then you're eating dairy.
If you eat dairy, then you're getting calcium.
Rosalinda eats yogurt.
Rosalinda is getting calcium.
500
Transitive property
If a=b and b=c then a=c
500
angle 6 and angle 7
Vertical angles
500
m angle LGK + m angle GKM = 180^circ
Same-side interior angle postulate