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Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

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Page 1: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Lesson 2.1 Lesson 2.1 ConditionalConditionalStatementsStatements

Page 2: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Conditional StatementConditional Statement

Two parts: Two parts: hypothesis and hypothesis and conclusionconclusion

If-then formIf-then form

Page 3: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Ex. If it is noon Ex. If it is noon in Philadelphia, in Philadelphia, then it is 9 A.M. then it is 9 A.M. in Los Angeles.in Los Angeles.

Page 4: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

““if” contains if” contains hypothesishypothesis

“then” contains “then” contains conclusionconclusion

Page 5: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Example 1Example 1

Write the statements in Write the statements in if-then form.if-then form.

Page 6: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

1. A number 1. A number divisible by 9 is divisible by 9 is

also divisible by 3.also divisible by 3.

Page 7: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

If a number is If a number is divisible by 9, divisible by 9,

then it is divisible then it is divisible by 3.by 3.

Page 8: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

2. All mammals 2. All mammals

breathe oxygenbreathe oxygen..

Page 9: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

If an animal is a If an animal is a mammal, then it mammal, then it

breathes oxygen.breathes oxygen.

Page 10: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

3. Two points are 3. Two points are collinear if they lie collinear if they lie on the same line.on the same line.

Page 11: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

If two points lie If two points lie on the same line, on the same line,

then they are then they are collinear.collinear.

Page 12: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Conditional Conditional Statements can be Statements can be

true or false. If true or false. If they are false, we they are false, we

must find a must find a counterexample.counterexample.

Page 13: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Example 2Example 2

Determine if the statement Determine if the statement is true or false. If it is false, is true or false. If it is false, find a counterexamplefind a counterexample

Page 14: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

If a point is If a point is distinct, then it distinct, then it

may lie on more may lie on more than one line.than one line.

Page 15: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

If xIf x22=16, then x=4=16, then x=4

Page 16: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

If a number is If a number is odd, then it is odd, then it is divisible by 3.divisible by 3.

Page 17: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Converse: formed Converse: formed by switching the by switching the hypothesis and hypothesis and

conclusionconclusion“flip-flop”“flip-flop”

Page 18: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Statement: If you see lightning, then you hear thunder?

Converse: If you hear thunder, then you see lightning.

Are both these true?

Page 19: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

If 2 segments are If 2 segments are congruent, then congruent, then they have the they have the same length.same length.

Page 20: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Converse: If two Converse: If two segments have segments have

the same length, the same length, then they are then they are

congruent.congruent.

Page 21: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

If an angle is If an angle is acute, then its acute, then its

measure is less measure is less than 90 degrees.than 90 degrees.

Page 22: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Converse: If an Converse: If an angle measures angle measures less than 90less than 90°°, ,

then it is acute.then it is acute.

Page 23: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Inverse: negate Inverse: negate the hypothesis the hypothesis and conclusionand conclusion

Page 24: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Contrapositive: Contrapositive: Negate the Negate the converseconverse

“Negative flip-flop“Negative flip-flop””

Page 25: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

If m<A=120If m<A=120°° degrees, then the degrees, then the angle is obtuse.angle is obtuse.

Page 26: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Inverse: Inverse: If m<AIf m<A≠≠120120°°

degrees, then the degrees, then the angle is not obtuse.angle is not obtuse.

Page 27: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Converse:Converse: If the angle is If the angle is obtuse, then obtuse, then m<A=120m<A=120°°..

Page 28: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Contrapositive:Contrapositive: If the angle is not If the angle is not

obtuse, then obtuse, then m<A m<A ≠≠ 120. 120.

Page 29: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Statement: If Statement: If m<P=90m<P=90°°, then , then

<P is a right <P is a right angle.angle.

Page 30: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Inverse:Inverse: If m<P If m<P ≠≠ 90 90°°, ,

then <P is not a then <P is not a right angle.right angle.

Page 31: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Converse:Converse: If <P is a right If <P is a right

angle, then angle, then m<P=90. m<P=90.

Page 32: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Contrapositive:Contrapositive: If <P is not a If <P is not a

right angle, then right angle, then m<P m<P ≠≠ 90. 90.

Page 33: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Statement:Statement:

If an animal is a fish, then it can If an animal is a fish, then it can swim.swim.

Page 34: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

InverseInverse

If an animal is not a fish, then it If an animal is not a fish, then it can not swim.can not swim.

Page 35: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

ConverseConverse

If an animal can swim, then If an animal can swim, then it is a fish.it is a fish.

Page 36: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

ContrapositiveContrapositive

If an animal can’t swim, then If an animal can’t swim, then it is not a fish.it is not a fish.

Page 37: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

StatementStatement

If x=y, then 3x=3y.If x=y, then 3x=3y.

Page 38: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

InverseInverse

If xIf x≠y, then 3x ≠3y.≠y, then 3x ≠3y.

Page 39: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

ConverseConverse

If 3x=3y, then x=y.If 3x=3y, then x=y.

Page 40: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

ContrapositiveContrapositive

If 3x If 3x ≠3y, then x ≠y.≠3y, then x ≠y.

Page 41: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Equivalent Equivalent Statements: Statements:

two statements are two statements are both true or both both true or both

false.false.

Page 42: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Postulate 5Postulate 5

Through any 2 points, there Through any 2 points, there exists exactly one line.exists exactly one line.

Page 43: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Postulate 6Postulate 6

A line contains AT LEAST 2 A line contains AT LEAST 2 pointspoints

Page 44: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Postulate 7Postulate 7

If two lines intersect, If two lines intersect, then their intersection then their intersection is exactly one point.is exactly one point.

Page 45: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Postulate 8Postulate 8

Through any 3 Through any 3 NONCOLLINEAR points, NONCOLLINEAR points, there exists exactly one there exists exactly one plane.plane.

Page 46: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Postulate 9Postulate 9

A plane contains AT LEAST A plane contains AT LEAST 3 NONCOLLINEAR points.3 NONCOLLINEAR points.

Page 47: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Postulate 10Postulate 10

If two points lie in a plane, If two points lie in a plane, then the line containing then the line containing them also lies in the plane.them also lies in the plane.

Page 48: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Postulate 11Postulate 11

If two planes intersect, then If two planes intersect, then their intersection is a line.their intersection is a line.

Page 49: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Write postulate 5 in if-then form.Write postulate 5 in if-then form.

Through any 2 points, there exists Through any 2 points, there exists exactly one line.exactly one line.

If there are 2 points, then there If there are 2 points, then there exists exactly one line.exists exactly one line.

Page 50: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

InverseInverse

If there is not two points, If there is not two points, then there is not exactly one then there is not exactly one line.line.

Page 51: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

ConverseConverse

If there exists exactly one If there exists exactly one line, then there are 2 points.line, then there are 2 points.

Page 52: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

ContrapositiveContrapositive

If there is not exactly one If there is not exactly one line, then there is not 2 line, then there is not 2 points.points.

Page 53: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

Postulate 8Postulate 8

Through any 3 noncollinear Through any 3 noncollinear points, there exists exactly one points, there exists exactly one plane.plane.

If there are 3 noncollinear points, If there are 3 noncollinear points, then there exists exactly one then there exists exactly one plane.plane.

Page 54: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

InverseInverse

If there are not 3 If there are not 3 noncollinear points, then noncollinear points, then there is not exactly one there is not exactly one plane.plane.

Page 55: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

ConverseConverse

If there exists exactly one If there exists exactly one plane, then there are 3 plane, then there are 3 noncollinear points.noncollinear points.

Page 56: Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

ContrapositiveContrapositive

If there is not exactly one If there is not exactly one plane, then there are not 3 plane, then there are not 3 noncollinear points.noncollinear points.


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