2Conditional Statement A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If ..Hypothesis, then… Conclusion
3If - then“If you don’t eat your meat, then you can’t have any pudding”Pink FloydIf you study the notes in Geometry, then you have a much better chance of passing a test or quiz.- Me
4Here another conditional statement If x = 3, then x + 4 = 7x = 3 is the hypothesis; label as px + 4 = 7 is the conclusion; label as qIf p then q
5The Hypothesis must always be TRUE If the hypothesis is not true, then strange things will happen. “If pigs fly, then I will win the Lottery”.
6The Counter ExampleCounter 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?
7An Algebra Counter Example 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.
9How do you make a Counter Example? You would Negation the conclusion. Negation is writing the negative or opposite of the statement. X = 20, negation x ≠ 20 NEVER NEGATE THE HYPOTHESIS
10Since 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
11Converse is more then a Shoe! 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
12If you Negate the Original Conditional Statement you have the Inverse If x = 3, then 2x + 4 = 10 Original Conditional If x ≠ 3, then 2x + 4 ≠ 10 Inverse To find the Inverse; Negate the Hypothesis and the Conclusion. In this example both this statement are True.
13If you Negate the Converse, then you get another type of statement. 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
14Equivalent statements 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
15Which are both True or False? 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.
16Lets review the type of Statements 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
17Lets review the type of Statements 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)
18Postulates about Points, Lines and Planes We have had 4 Postulate before what are they? What is a Postulate?
19Postulates about Points, Lines and Planes We have had 4 Postulate before what are they? Ruler Postulate Segment Addition Postulate Protractor Postulate Angle Postulate
20Postulates about Points, Lines and Planes 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.
22Why do most stools have three legs? 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.
232 more Postulates about Points, Lines and Planes 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.