Conditionals
Biconditionals
Algebraic Proof Reasons
Geometric Proof Reasons
Parallel Lines Proof Reasons
100
The if part of a conditional is the hypothesis.
The then part of a conditional is the ________.
conclusion
100
A biconditional is only true if the conditional and it's __________ is true.
converse
100
x+5=14
x=9
What is the reason for this step?
Subtraction Property of Equality
100
∠1 ≅ ∠2 and ∠2 ≅ ∠3
Using transitive property... what conclusion can be drawn?
∠1 ≅ ∠3
100
Given: q||s
Which reason justifies why angle 3 and 6 are congruent?
Alternate Interior Angles
200
A conditional statement is also known as an ______ statement.
if/then
200
Is this biconditional true or false?
If false, state a counterexample.
A shape is a trapezoid if and only if it has four sides.
False: rectangle
200
4x+7+8x=19
12x+7=19
What is the reason for this step?
Simplify or combine like terms
200
Fill in the reasons. 
Given: M is the midpoint of AB.
1. AM=MB 1. ______________________
2. 4x+13=3x+17 2.____________________
Definition of midpoint
Substitution
200
What reason justrifies why angle 1 and 2 are congruent?
Corresponding Angles
300
Write the statement as a conditional.
Angles that form a linear pair are supplementary.
If two angles form a linear pair, then they are supplementary.
300
Is the CONVERSE of this statement true or false? If false, give a counterexample.
If you live in in Missouri, then you live in the United States.
False, Texas
300
33=3(2x+7) given
33=6x+21 _______________
12=6x Subtraction POE
2=x Division POE
x=2 ___________________
Distributive property and symmetric property
300
What reason matches this step?
QR+RS=QS
Segment Addition
300
Which statement matches this reason?
m∠4+m∠7=180
Same-Side Interior Angles
400
Write the statement as a conditional.
You live in Missouri if you live in Sedalia.
If you live in Sedalia, then you live in Missouri.
400
If it is raining, then I use an umbrella.
If I use an umbrella, then it is raining.
Write this statement as a biconditional.
It is raining if and only if I am using an umbrella.
400
Given 3x+2=8
Prove: x=2
3x+2=8 given
3x=6 Subtraction property of equality
x=2 division property of equality
400
Which reason matches this step?
m∠AOB+m∠BOC=m∠AOC
Angle Addition
400
Fill in the reasons.
1. ∠1≅ ∠9 Reason: ________________
2. ∠9≅ ∠16 Reason: _______________
3. ∠1≅ ∠16 Reason: _______________
1. Corresponding 2. Alternate Exterior 3. Transitive Property
500
Determine if the conditional is true or false. If false, give a counter example.
If two angles are supplementary, then one angle is acute and one is obtuse.
False, two right angles
500
A line bisects a segment if and only if it intersects at its midpoint.
Write the two statements that form this biconditional.
Then determine if the biconditional is true or false.
If a line bisects a segment, then it intersects at the segments midpoint.
If a line intersects at a segments midpoint, then it bisects the line.
True
500
Given: 4(x+2) +6x = 22
Prove: x=2
4(x+2)+6x=22 given
4x+8+6x=22 distributive property
10x+8=22 simplify
10x=14 subtraction property of equality
x=1.4 division property of equality
500
Fill in the reasons for each step.
1. ∠ABD and ∠DBC are supplementary
Reason: ___________________
2. m∠ABD+m∠DBC = 180
Reason: ___________________
1. Linear Pair
2. Definition of Supplementary
500
Which lines would be parallel if angle 2 and 3 were congruent? What reason?
p||r, Converse of the Alternate Exterior Angles Theorem