2.1 Conditional Statements. Conditional Statement  Conditional statement has two parts, hypothesis and a conclusion.  If _, then.

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Presentation transcript:

2.1 Conditional Statements

Conditional Statement  Conditional statement has two parts, hypothesis and a conclusion.  If _____________, then____________. hypothesis conclusion

Rewrite in If-Then form AA number divisible by 9 is also divisible by 3. IIf a number is divisible by 9, then it is divisible by 3. TTwo points are collinear if they lie on the same line. IIf two points lie on the same line, then they are collinear.

Writing a Counterexample  Write a counterexample to show that the following conditional statement is false.  If x 2 = 16, then x = 4.

Converse TTwo points are collinear if they lie on the same line. IIf two points are collinear, then they lie on the same line. IIf two points lie on the same line, then they are collinear. Conditional Statement Converse

 A statement can be altered by negation, that is, by writing the negative of the statement.  Statement: m<A = 30°  Negation: m < A ≠ 30°  Statement: <A is acute.  Negation: <A is not acute.

Inverse  If two points lie on the same line, then they are collinear.  If two points do not lie on the same line, then they are not collinear. Conditional Inverse

Contrapositive  If two points lie on the same line, then they are collinear.  If two points are not collinear, then they do not lie on the same line. Conditional Contrapositive

 When two statements are both true or both false, they are called equivalent statements.  A conditional statement is equivalent to its contrapositive.  The inverse and converse of any conditional statement are equivalent.

 Write the  a) inverse  b) converse  c) contrapositive If there is snow on the ground, then flowers are not in bloom. a) If there is no snow on the ground, then flowers are in bloom. b) If flowers are not in bloom, then there is snow on the ground. c) If flowers are in bloom, then there is no snow on the ground.

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.  Postulate 7  If two lines intersect, then their intersection is exactly one point.

 Postulate 8  Through any three noncollinear points there exists exactly one plane.  Postulate 9  A plane contains at least three noncollinear points.  Postulate 10  If two points lie in a plane, then the line containing them lies in the plane.

 Postulate 11  If two planes intersect, then their intersection is a line.

Review  Write the converse of the conditional statement.  If x = 3, then y = 7.  If Carrie joins the softball team, then Mary will join.  If two angles are vertical, then their measures are equal.