Conjectures and Counterexamples
Conditions May Apply
Show me the Proof
Algebra Edition
Algebra Edition
Show me the Proof
Segment Edition
Segment Edition
Show me the Proof
Angle Edition
Angle Edition
100
Determine if the conjecture is true or false. If false, provide a counter example.
All people from Dallas are also from Texas.
True
100
What is a conditional statement?
If - Then statement
100
What definition, property, or postulate is demonstrated?
If BH = MU, then MU = BH
Symmetric Property of Equality
100
What is the definition of a midpoint?
A point that divides a segment into 2 congruent segments.
100
Which of the following are vertical angles?
angle XYV and angle WYZ or angle XYW and angleVYZ
200
Determine if the conjecture is true or false. If false, provide a counter example.
"All even numbers are evenly divisible by 2"
True
200
For the following statements, what is the Inverse?
p: I eat many cookies
q: I am very happy
If I don't eat many cookies, then I'm not very happy
200
What property, definition, or postulate is being demonstrated?
If HG = FD, then HG + PI = FD + PI
Addition Property
200
What property, definition, or postulate is being demonstrated?
If G is between B and F, then BG + GF = BF
Segment Addition Postulate
200
What property, definition or postulate is being demonstrated?
Definition of Perpendicular
300
Determine if the conjecture is true or false. If false, provide a counter example.
"All multiples of 2 are also multiples of 4"
False 6 is a multiple of 2 but not a multiple of 4
300
For the following statements what is the contrapositive?
p: Two angles are a linear pair
q: Two angles are supplementary
If two angles are not supplementary, then those two angles are not a linear pair
300
What property, definition, or postulate is being demonstrated?
Division Property
300
What is the reason for statement 7?
Definition of Congruence
300
What property, definition, or postulate is being demonstrated?
Angle Addition Postulate
400
Determine if the conjecture is true or false. If false, provide a counter example.
"All whole numbers are also natural numbers"
False, 0
400
What 2 statements (conditional, inverse, converse, contrapositive) must be true in order for a conditional to be biconditional?
conditional and converse
400
What is the reason for statement 6?
Simplify
400
What is the reason for statement 6?
Transitive Property
400
If you are Given
m angle 1 + m angle 3 = 90^o
by what reason can you state that
angle 1 and angle3
are complementary?
Definition of Complementary Angles
500
Determine if the conjecture is true or false. If false, provide a counter example.
"All angles must be adjacent in order to be supplementary"
False, an angle that is 73 degrees and 107 degrees are supplementary but they don't necessarily need to be adjacent
500
Would the following statements create a biconditional statement that is true
p: The measures of 2 angles add to 90 degrees
q: 2 angles are complementary
Yes, the measures of 2 angles add to 90 degrees if and only if the 2 angles are complementary
500
What would be your next statement?
2c = 8
500
What is the reason for statement 4?
Substitution Property
500
What would be the reason for number 6?
Transitive Property