If-Then Statements
A statement in two parts Hypothesis and
Conclusion.
Written in the If-Then form
If ..Hypothesis, then… Conclusion
“If you don’t eat your meat, then you can’t have
any pudding”
◦ Pink Floyd
If you study the notes in Geometry, then you have a
much better chance of passing a test or quiz.
- Me
If x = 3, then x + 4 = 7
x = 3 is the hypothesis; label as p
x + 4 = 7 is the conclusion; label as q
If p then q
If the hypothesis is not true, then strange
things will happen.
“If pigs fly, then I will win the Lottery”.
Counter Examples are very powerful. With one
counter example you can stop an argument
with one thought.
“If everyone likes snow days, then everyone
likes cold weather”
Is there someone here in the class that does
not like cold weather?
If x2 = 25, then x = 5
Is this true? (5)2 = 25
but the counter example shows ( - 5)2 = 25
So the conditional statement is false.
Since – 5 would also work.
Conditional statements can be true or false.
You would Negation the conclusion.
Negation is writing the negative or opposite of
the statement.
X = 20, negation x ≠ 20
NEVER NEGATE THE HYPOTHESIS
Since Mr. Grosz go to a High School every week
day, then he must be a high school student.
Negation: Mr. Grosz is not a High School
student.
The Hypothesis is still true.
THE HYPOTHESIS MUST ALWAYS STAY TRUE
The Converse is the switching of the
hypothesis and the conclusion.
If the statement was “If p, then q”, then it
becomes “If q, then p”.
If x = 3, then x + 4 = 7.
The Converse
If x + 4 = 7, then x = 3
If you Negate the Original Conditional
Statement you have the Inverse
If x = 3, then 2x + 4 = 10
If x ≠ 3, then 2x + 4 ≠ 10
Original Conditional
Inverse
To find the Inverse; Negate the Hypothesis and the
Conclusion.
In this example both this statement are True.
The Contrapositive is the negation of the
conclusion and hypothesis of the converse.
If x = 3, then 2x + 4 = 10
Original Conditional
If x ≠ 3, then 2x + 4 ≠ 10
Inverse
If 2x + 4 = 10 ,then x = 3
Converse
If 2x + 4 ≠ 10, then x ≠ 3
Contrapositive
Statements that are both true or false.
Conditional Statement
x = 2, then x2 = 4 True
Inverse
x≠2, then x2≠4
False
Converse
x2=4, then x = 2 False
Contrapositive
x2≠4, then x≠2
True
The Condition Statement and the
Contrapositive are both True.
These statements will always have the same
true table.
(Meaning they are both true or false)
The Inverse and the Converse have the same
true table.
If you feed it, then it will grow.
If you don’t feed it, then it will not grow
If it will grow, then you feed it
If it will not grow, then you did not feed it
If you feed it, then it will grow.
( Conditional statement)
If you don’t feed it, then it will not grow
(Inverse)
If it will grow, then you feed it
(Converse)
If it will not grow, then you did not feed it
(Contrapositive)
We have had 4 Postulate before what are they?
What is a Postulate?
We have had 4 Postulate before what are they?
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Postulate
Postulates without names
Through any two points there exists exactly
one line.
A line contains at least 2 points.
If two lines intersect, then their intersection is
exactly one point.
Answer
Through any three noncollinear points there
exist exactly one plane.
You want a stool to only be only in one plane,
why?
A plane contains at least three noncollinear
points.
If two points lie in a plane, then the line
containing the points lie in the plane.
( it nails the line to the plane)
If two planes intersect then their intersection is
a line.
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# 9 – 17 odd,
18, 20, 22, 29 – 34,
36, 38, 40, 41,
44, 48, 52