Negation and Truth Tables
What is the negation of the following statement:
"A triangle has three sides."
"A triangle does not have three sides."
"All alternate exterior angles in parallel lines cut by a transversal are congruent."
"If two lines are parallel and cut by a transversal, the the alternate exterior angles are congruent."
P usually represents the _________ from the conditional statement.
Hypothesis
How do you make a converse of a conditional statement?
∠ A and ∠ B have the same measure. What reason could you use to state ∠ A≅ ∠ B?
Definition of Congruent
What is the negation of this conditional:
"If two angles are vertical, then they are congruent."
If two angles are not vertical, then they are not congruent.
Given the conditional statement decide if the argument is valid or invalid.
"If a point on a segment is the midpoint, then it divides the segment into two equal parts."
A point on a segment is the midpoint.
So, it divides the segment into two equal parts.
Valid
What does the tilde (~) represent?
What is the converse of
"If two parallel lines are cut by a transversal, then each corresponding angles are congruent."
If each corresponding angles are congruent, then two parallel lines are cut by a transversal.
Identify the postulate:
DE +EF =DF
Segment Addition Postulate
What is the negation of this conditional:
If there are more than 15 students in the class, then the class is not precalculus.
If there are not more than 15 students in the class, then the class is precalculus.
Provide a counterexample for the following statement.
"If two angles have a sum of 180 degrees, then they are a linear pair."
Possible answer:
Two angles could be supplementary but not necessarily linear.
What does this notation represent?
q→p
The converse.
What is the inverse of
"If two lines are parallel and cut by a transversal, then the alternate exterior angles are congruent."
"If two lines are not parallel and cut by a transversal, then the alternate exterior angles are not congruent."
What could be the next statement after knowing that ∠ A and ∠ B are a linear pair?
Possible answer:
∠ A + ∠ B = 180
What is the correct order for the missing values in this truth table?
(Image Truth Table 1)
F, T
To get full credit when writing any kind of statement in Wiris, you have to do these two things.
C ______ and p_______.
Capitalize and punctuate.
What does this notation represent?
~q→~p
The contrapositive.
What is the contrapositive of the following statement.
"If two lines are parallel and cut by a transversal, then the alternate exterior angles are congruent."
If the alternate exterior angles are not congruent, then two lines are not parallel and not cut by a transversal.
m∠A - 90=70 is given. What reason can we give for the next statement:
m∠A=160.
Addition Property of Equality
What is the correct order for the missing values in this truth table?
(Image Truth Table 2)
T,T,T,F
What is the biconditional for the following statement:
"If two points lie on the same straight line, then they are collinear."
Two points lie on the same straight line if and only if they are collinear.
How do you say this notation and what does it represent?
~p→~q
If not p then not q. It is the inverse.
Which statements need to always be true to make a biconditional?
Conditional and converse.
If ∠ 1 and ∠ 2 are supplementary and ∠ 2 and ∠3 are supplementary, how can we say ∠ 1 ≅ ∠ 3
Congruent supplements or substitution