Reasoning, Conjectures, & Counterexamples
Compound Statements
Algebraic Proofs
Segment Proofs
Angle Proofs
100
All cars use gas. True or False(Counterexample)
False; Hybrids
100
What symbol is used for a conjuction?
^^
100
a=a
Reflexive
100
Justify this statement:
If PQ+RS=PS and RS=XY, then PQ+XY=PS
Substitution
100
If point D is in the interior of
/_ABC
m/_ABD+m/_DBC=m/_ABC
Angle Addition Postulate
200
Finish the series: 2, 5, 11, 23, __, __, __
47, 95, 191
200
What does this symbol mean?
~
Negation
200
I use this property when I add the same thing to both sides of an equation.
Addition Property
200
If
AB=CD
, then
bar(AB)~=bar(CD)
Definition of Congruence
200
Complementary⟷Sum is 90°
Definition of Complementary Angles
300
True or False: Multiples of 3 are always multiples of 6.
False.
300
p: Christmas is in July.
q: Redstreaks are red.
Write the statement for
~p ^^ q
Christmas is not in July and redstreaks are red.
300
Justify this statement:
If
-3(2x+7)=-29-4x
then
-6x-21=-29-4x
Distributive Property
300
If A, B, and C are collinear points with B between A and C, then:
AB+BC=AC
Segment Addition Postulate
300
If two angles are supplementary to the same angle, then they are congruent.
Congruent Supplements Theorem
400
"Multiples of 3 are always multiples of 6" is false. what is a counterexample?
15, 9, 27
400
How many statements must be true in a conjunction?
Both statements
400
A=B, B=C, A=C
Transitive Property
400
If LP=PN, and L, N, and P are collinear, then P is the midpoint of LN
Definition Of A Midpoint
400
If ∠S and ∠T form a right angle, then ∠S and ∠T are complementary.
Complement Theorem
500
Why is the statement "Supplementary angles are never congruent" false? Draw the counterexample.
500
p: All vegetables are green.
q: All integers are natural numbers.
Write out the following compound statement correctly and give the correct truth value.
~p v ~q
All vegetables are not green or all integers are not natural numbers.
True
500
This is the reason I use when I combine like terms.
Simplify
500
If RS=TU, then RS+XY=TU+XY
Addition Property
500
What is the definition of an angle bisector?
An angle bisector divides an angle into two equal parts.