Day 3. Warm Up. Find the distance and midpoint between the two points below. Distance: . **Remember: AB = distance between A and B** AB = length of = segment between A and B (Notation) Distance: on a # line: on a coordinate plane: Pythagorean Theorem or
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Find the distance and midpoint between the two points below
**Remember: AB = distance between A and B**
AB = length of
= segment between A and B (Notation)
Distance: on a # line:
on a coordinate plane:
Pythagorean Theorem or
On a # line:
On a coordinate plane:
1. sqrt(41) = 6.4 2. (6.5, 6)
“If you are not completely satisfied, then your money will be refunded.”
“If a figure is a rectangle, then it has four right angles.”
“If an integer ends with 0, then it is divisible by 5.”
A conditional can have a truth value of true or false.
To show that a conditional is true, you must show that every time the hypothesis is true, the conclusion is also true.
To show that a conditional is false, you need to only find one counterexample
Negation: ABC is not obtuse
Negation: mXYZ is not more than 70
Conditional: If a figure is a square, then it is a rectangle.
Definition: The inverse of a conditional statement negates both the hypothesis and the conclusion
Inverse: If , then
Definition: The contrapositive of a conditional statement switches the hypothesis and the conclusion and negates both.
a figure is not a square
it is not a rectangle
it is not a square
a figure is not a rectangle
A conditional statement and its converse may or may not have the same truth values.
A conditional statement and its inverse may or may not have the same truth values
HOWEVER, a conditional statement and its contrapositive will ALWAYS have the same truth value. They are equivalent statements.
Equivalent Statementshave the same truth value
When a conditional and its converse are true, you can combine them as a true biconditional. This is a statement you get by connecting the conditional and its converse with the word and.
You can also write a biconditional by joining the two parts of each conditional with the phrase if and only if
A biconditional combines p → q and q → p as p ↔ q.
Scrapbook Project due Friday
Distance/Midpoint Mini-Project due Sept 18