2.1 Conditional Statements Goal 1: Recognizing Conditional Statements Goal 2: Using Point, Line, and Plane Postulates CAS 1,3.

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Presentation transcript:

2.1 Conditional Statements Goal 1: Recognizing Conditional Statements Goal 2: Using Point, Line, and Plane Postulates CAS 1,3

Conditional Statement A statement that has two parts, the hypothesis and conclusion, written in the “If- then” form. Ex. 1  If the moon is visible, then it is night time. hypothesis conclusion ****Note- the words “if” and “then” are not included in the hypothesis and the conclusion

True or False Conditional statements can be either true or false. A conditional statement is: TRUE- if it is true for ALL possible cases. FALSE- if you find even ONE counterexample where the conclusion does not have to be true.  Re-read example 1 from your notes. Can you think of one counterexample to establish if it is TRUE or FALSE.

TRUE or FALSE (continued-) If, then Is this TRUE or FALSE?

Converse of a Conditional Statement The converse of a conditional statement is formed by switching the hypothesis and conclusion.  Ex 2. Statement: If you study, then you are an A student. Converse: If you are an A student, then you study.

Converse (continued-) What is the converse of the following conditional statement?  Ex. 3 If a number is divisible by two, then the number is an even number.

Negation To negate either the hypothesis or conclusion of a conditional statement you say “is not” or “isn’t” in front of it  Ex. 4 If a flower grows, then it is alive. The negation of the hypothesis is:  “a flower does not grow” The negation of the conclusion is:  “it is not alive”

Inverse of a Conditional Statement When you negate both the hypothesis and conclusion of a conditional statement.  Ex. 5 Conditional Statement:  If an angle is 90 degrees, then it is a right angle. Inverse:  If an angle is not 90 degrees, then it is not a right angle.

Contrapositive of a Conditional Statement When you negate the entire conditional statement (inverse) and apply the converse. Ex. 6  Conditional Statement: If a shape has three sides, then it is a triangle.  Contrapositive: If a shape is not a triangle, then it does not have three sides.  ****NOTE- Sometimes when re-writing the statements you must change the order of some words to work out the tenses in English.

Equivalent Statements If two statements are both true or both false, then they are called equivalent statements. ***NOTE- Two important relationships. 1. A conditional statement is equivalent to its contrapositive. 2. The inverse and converse of any conditional statement are equivalent.

Equivalent Statements (continued-) Original Statement If, then is acute Inverse If, then is not acute Converse If is acute, then Contrapositive If is not acute, then

Point, Line, and Plane Postulates Postulate 5 Through any two points there exists exactly one line. Postulate 6 A line contains at least two points.

Point, Line, and Plane Postulates (continued-) Postulate 7If two lines intersect, then their intersection is exactly one point

Point, Line, and Plane Postulates (continued-) Postulate 8Through any three noncollinear points there exists exactly one plane Postulate 9A plane contains at least three noncollinear points M A B C

Point, Line, and Plane Postulates (continued-) Postulate 10If two points lie in a plane, then the line containing them lies in the plane.

Point, Line, and Plane Postulates (continued-) Postulate 11If two planes intersect, then their intersection is a line.