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Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements...

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Conditional statements
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Page 1: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Conditional statements

Page 2: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Conditional statements

If an angle is a right angle, then it has a measure of 90º.

Page 3: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Conditional statements

If an angle is a right angle, then it has a measure of 90º.

~p ("not p") is the negation of p.

Page 4: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Conditional statements

If an angle is a right angle, then it has a measure of 90º.

~p ("not p") is the negation of p.~p is "An angle is not a right

angle."

Page 5: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Conditional statements

If an angle is a right angle, then it has a measure of 90º.

~p ("not p") is the negation of p.~p is "An angle is not a right

angle."~q is "An angle does not have a

measure of 90º."

Page 6: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement: qp

Page 7: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

qp

q p

Page 8: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Page 9: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

Page 10: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If an angle is a right angle,then it has a measure of 90º.

Page 11: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If an angle has a measure of 90º,then it is a right angle.

If an angle is a right angle,then it has a measure of 90º.

Page 12: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If an angle has a measure of 90º,then it is a right angle.

If an angle is a right angle,then it has a measure of 90º.

If an angle is a not right angle,then it does not have a measure of 90º.

Page 13: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If an angle has a measure of 90º,then it is a right angle.

If an angle is a right angle,then it has a measure of 90º.

If an angle is a not right angle,then it does not have a measure of 90º.

If an angle does not have a measure of 90º,then it is not a right angle.

Page 14: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If an angle has a measure of 90º,then it is a right angle.

If an angle is a right angle,then it has a measure of 90º.

If an angle is a not right angle,then it does not have a measure of 90º.

If an angle does not have a measure of 90º,then it is not a right angle.

true

Page 15: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If an angle has a measure of 90º,then it is a right angle.

If an angle is a right angle,then it has a measure of 90º.

If an angle is a not right angle,then it does not have a measure of 90º.

If an angle does not have a measure of 90º,then it is not a right angle.

true

true

Page 16: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If an angle has a measure of 90º,then it is a right angle.

If an angle is a right angle,then it has a measure of 90º.

If an angle is a not right angle,then it does not have a measure of 90º.

If an angle does not have a measure of 90º,then it is not a right angle.

true

true

true

Page 17: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If an angle has a measure of 90º,then it is a right angle.

If an angle is a right angle,then it has a measure of 90º.

If an angle is a not right angle,then it does not have a measure of 90º.

If an angle does not have a measure of 90º,then it is not a right angle.

true

true

true

true

Page 18: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If two angles are right angles,then they are congruent.

true

Page 19: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If two angles are right angles,then they are congruent.

true

falseIf two angles are congurent,then they are right angles.

Page 20: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If two angles are right angles,then they are congruent.

true

false

false

If two angles are congurent,then they are right angles.

If two angles are not right angles,then they are not congruent.

Page 21: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If two angles are right angles,then they are congruent.

true

false

false

true

If two angles are congurent,then they are right angles.

If two angles are not congurent,then they are not (both) right angles.

If two angles are not right angles,then they are not congruent.

Page 22: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If you live in Chicago,then you live in Illinois.

true

Page 23: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If you live in Chicago,then you live in Illinois.

true

falseIf you live in Illinois,

then you live in Chicago.

Page 24: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If you live in Chicago,then you live in Illinois.

true

false

false

If you live in Illinois,then you live in Chicago.

If you do not live in Chicago,then you do not live in Illinois.

Page 25: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If you live in Chicago,then you live in Illinois.

true

false

false

true

If you live in Illinois,then you live in Chicago.

If you do not live in Illinois,then you do not live in Chicago.

If you do not live in Chicago,then you do not live in Illinois.

Page 26: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

falseIf you live in Illinois,

then you live in Chicago.

Page 27: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If you live in Chicago,then you live in Illinois.

true

falseIf you live in Illinois,

then you live in Chicago.

Page 28: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If you live in Chicago,then you live in Illinois.

true

false

true

If you live in Illinois,then you live in Chicago.

If you do not live in Illinois,then you do not live in Chicago.

Page 29: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If you live in Chicago,then you live in Illinois.

true

false

false

true

If you live in Illinois,then you live in Chicago.

If you do not live in Illinois,then you do not live in Chicago.

If you do not live in Chicago,then you do not live in Illinois.

Page 30: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

falseIf you live in Indiana

then you live in Chicago.

Page 31: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If you live in Chicago,then you live in Indiana.

falseIf you live in Indiana

then you live in Chicago.false

Page 32: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If you live in Chicago,then you live in Indiana.

falseIf you live in Indiana

then you live in Chicago.

If you do not live in Indianathen you do not live in Chicago.

false

false

Page 33: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Statement:

Converse:

Inverse: ~p ~q

qp

q p

Contrapositive: ~p~q

If you live in Chicago,then you live in Indiana.

false

false

If you live in Indianathen you live in Chicago.

If you do not live in Indianathen you do not live in Chicago.

If you do not live in Chicago,then you do not live in Indiana.

false

false

Page 34: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Theorem 3: If a conditional statement is true, then the

contrapositive of the statement is also true.

(If p, then q If ~p, then ~q)

Page 35: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Theorem 3: If a conditional statement is true, then the

contrapositive of the statement is also true.

(If p, then q If ~p, then ~q)

means "if and only if"

Page 36: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Theorem 3: If a conditional statement is true, then the

contrapositive of the statement is also true.

(If p, then q If ~p, then ~q)

means "if and only if"

"iff" means "if and only if"

Page 37: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Circle diagramsVenn diagramsEuler diagrams

Page 38: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Circle diagramsVenn diagramsEuler diagrams

Circle A representspeople who live inChicago.A

Page 39: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Circle diagramsVenn diagramsEuler diagrams

Circle A representspeople who live inChicago.

Circle B representspeople who live inIllinois.

AB

Page 40: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Circle diagramsVenn diagramsEuler diagrams

Circle A representspeople who live inChicago.

Circle B representspeople who live inIllinois.

AB

Mayor of Chicago

Page 41: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Circle diagramsVenn diagramsEuler diagrams

Circle A representspeople who live inChicago.

Circle B representspeople who live inIllinois.

AB

Mayor of Chicago

Narrator

Page 42: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Circle A representspeople who live inChicago.

A

Page 43: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Circle A representspeople who live inChicago.

Circle B representspeople who live inIllinois.

A

B

Page 44: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Circle A representspeople who live inChicago.

Circle B representspeople who live inIllinois.

A

BCircle C representspeople who live inthe USA.

C

Page 45: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Circle A representspeople who live inChicago.

Circle B representspeople who live inIllinois.

A

BCircle C representspeople who live inthe USA.

CCircle D representspeople who live inNorth America.

D

Page 46: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Chains of Reasoning

Page 47: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Chains of Reasoning

If p q, and q r,then p r.

Page 48: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Chains of Reasoning

If p q, and q r,then p r.

If you live in Chicago, then you live in Illinois.

Page 49: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Chains of Reasoning

If p q, and q r,then p r.

If you live in Chicago, then you live in Illinois.If you live in Illinois, then you live in the USA.

Page 50: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Chains of Reasoning

If p q, and q r,then p r.

If you live in Chicago, then you live in Illinois.If you live in Illinois, then you live in the USA.

Conclusion: If you live in Chicago, then you live in the USA.

Page 51: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Chains of Reasoning

If p q, q r, and r s,then p s.

Page 52: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Chains of Reasoning

If p q, q r, and r s,then p s.

If you live in Chicago, then you live in Illinois.

Page 53: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Chains of Reasoning

If p q, q r, and r s,then p s.

If you live in Chicago, then you live in Illinois.If you live in Illinois, then you live in the USA.

Page 54: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Chains of Reasoning

If p q, q r, and r s,then p s.

If you live in Chicago, then you live in Illinois.If you live in Illinois, then you live in the USA.If you live in the USA then you live in North

America.

Page 55: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Chains of Reasoning

If p q, q r, and r s,then p s.

If you live in Chicago, then you live in Illinois.If you live in Illinois, then you live in the USA.If you live in the USA then you live in North

America.

Conclusion: If you live in Chicago, then you live in North America.

Page 56: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

If I study for many hours, I will do well in geometry.

Page 57: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

If I study for many hours, I will do well in geometry.

If I do well in geometry, I will get into a good college.

Page 58: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

If I study for many hours, I will do well in geometry.

If I do well in geometry, I will get into a good college.

If I get into a good college, I will be able get a high paying job.

Page 59: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

If I study for many hours, I will do well in geometry.

If I do well in geometry, I will get into a good college.

If I get into a good college, I will be able get a high paying job.

If I get a high paying job, I will become wealthy.

Page 60: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

If I study for many hours, I will do well in geometry.

If I do well in geometry, I will get into a good college.

If I get into a good college, I will be able get a high paying job.

If I get a high paying job, I will become wealthy.

Conclusion: If I study for many hours, I will become wealthy.

Page 61: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Conditional statement: qp

Page 62: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Conditional statement: qpConverse: q p

Page 63: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Conditional statement: qpConverse:

Inverse: ~p ~qq p

Page 64: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Conditional statement: qpConverse:

Inverse: ~p ~qq p

Contrapositive: ~p~q

Page 65: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Conditional statement: qpConverse:

Inverse: ~p ~qq p

Contrapositive: ~p~qCircle diagrams (also know as Venn

or Euler diagrams) help us depict conditional statements.

Page 66: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Conditional statement: qpConverse:

Inverse: ~p ~qq p

Contrapositive: ~p~qCircle diagrams (also know as Venn

or Euler diagrams) help us depict conditional statements.means "if and only if."

Page 67: Conditional statementstcanright.webmate.me/Geometry_Channel/Part_3g/Part_3g...Conditional statements If an angle is a right angle, then it has a measure of 90º. ~p ("not p") is the

Theorem 3: If a conditional statement is true, then the

contrapositive of the statement is also true.

(If p, then q If ~p, then ~q)


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