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Conditional Statements
Biconditional Statements
Properties
Algebra Proofs
!=~AlL MiXeD Up ~=!
100
Write the converse of the following: If Tom likes pizza, then Harry likes dogs.
What is "If Harry likes dogs, then Tom likes pizza."
100
Rewrite the biconditional as a conditional statement and its converse: Darth Vader is your father if and only if you are Luke.
What is If Darth Vader is your father then you are Luke.
100
Ifm
What is symmetric property of equality?
100
Solve and give reasons: 3x-11=23
What is 3x=24 (addition) x=8 (division)
100
Use inductive reasoning ... 100, 81, 64, 49, 36, ____, ____
What is 25, 16?
200
Write the inverse of the following: If cookies are good, then Mr. McMahon bakes cookies.
What is If cookies are not good, then Mr. McMahon did not bake cookies.
200
Determine if this biconditional is true. If false provide a counterexample: x=4 if and only if x+9=13
What is True
200
Property used to solve: 10x=100
What is Multiplication Property of equality?
200
Solve for x and give reasons: 7x+34=-9x+66
What is 16x+34=66 (addition) 16x=32 (subtraction) x=2 (division)
200
True or False - If False give counterexample. If an angle is obtuse, then it measures 120 degrees.
What is False- could be 100, 110, etc.
300
Write the contrapositive of the following statement: If snow is cold, then water isn't wet.
What is If water is wet, then snow is not cold.
300
Given the conditional statement, write the converse and the biconditional. Conditional: If pens write, then ducks quack.
What is converse- If ducks quack, then pens write. Bi -- Pens write if and only if ducks quack
300
Use multiplication property of equality to complete: If m
What is 250?
300
Solve for x and give reasons: 3(x-5)+22=5x-19
What is 3x-15+22=5x-19 (distributive) 3x+7=5x-19 (combine like terms) -2x+7=-19 (subtraction) -2x=-26 (subtraction) x=-13 (division)
300
GIVEN: B is the midpoint of AC. Prove: BC= AC What is our reason?
What is definition of midpoint?
400
Converse: If Adam likes apples, then penguins fly. Determine what the conditional statement is and write the inverse.
What is condtional- If penguins fly then Adam likes apples. Inverse- If penguins do not fly then Adam does not like apples.
400
Determine if this biconditional is true. If false provide a counterexample: x=4 if and only if x^2=16
What is False -4
400
Angles PQR and RQS form a linear pair. If m
What is 145?
400
Solve for x and give reasons AB=x+5, CD=3x-9, AB=EF and EF=CD (Draw image)
What is AB=CD (transitive) x+5=3x-9 (substitution) x=3x-14 (subtraction) -2x=-14 (subtraction) x=7 (division)
400
If the m
What is transitive property
500
Inverse: If puppies aren't cute, then the sky is blue. Determine the original conditional statement, and then write both the conditional, converse and contrapositive
What is conditional- If puppies are cute, then sky isn't blue Converse- If sky isn't blue then puppies are cute. Contrapositive- If sky is blue, then puppies are not cute.
500
Given a true conditional statement, determine if the converse is also true. If yes, write the biconditional. If no, give a counterexample. Conditional: If there is a seal, then it lives in the ocean.
What is Converse- If it lives in the ocean, then its a seal. False- could be another animal- Can not write a biconditional
500
P_____________R_________S PR= 3x+5 RS= 2x PS=30 Find x= Find PR= Find RS=
What is x=5, PR= 20, RS=10 ?
500
Solve for x and give reasons: If B is the midpoint of AC, and AB=3x+9 and AC=9x-84
What is AC=AB+BC (segment addition) AB=BC (definition of midpoints) AC=AB+AB (substitution) 9x-84=3x+9+3x+9 (substitution) 9x-84=6x+18 (combine like terms) 3x-84=18 (subtraction) 3x=102 (addition) x=34 (division)
500
If segment LC bisects
What is x=2,