Geometry Section 2.1 Conditional Statements NCSCOS: (2.01; 2.02) Ms. Vasili.

GeometryGeometrySection 2.1Section 2.1

Conditional StatementsConditional Statements

NCSCOS: (2.01; 2.02)NCSCOS: (2.01; 2.02)

Ms. VasiliMs. Vasili

Lesson Opener – Conditional Lesson Opener – Conditional StatementsStatements

Beagles

Animals

Dogs

Hartford

Venn Diagram

Then and Now: In the pursuit of Then and Now: In the pursuit of justice justice

A guild of lawyers and their apprentices first A guild of lawyers and their apprentices first appeared in England in the 14appeared in England in the 14 thth century. Since century. Since that time, the legal profession has spread that time, the legal profession has spread around the world. According to the around the world. According to the Occupational Outlook Handbook, lawyers and Occupational Outlook Handbook, lawyers and judges held approximately 716,000 jobs in the judges held approximately 716,000 jobs in the U.S in 1992. What about today ( research)? U.S in 1992. What about today ( research)?

Continue: In the persuit of Continue: In the persuit of justice justice

Lawyers may act as legal advisers to or Lawyers may act as legal advisers to or advocates for their clients. The details of the advocates for their clients. The details of the job depend on the lawyer’s specialization. But job depend on the lawyer’s specialization. But no matter their role, all lawyers must interpret no matter their role, all lawyers must interpret the law and apply it to their client’s situations. the law and apply it to their client’s situations. To interpret the law in specific situations, To interpret the law in specific situations, lawyers must be skillful in logical thinking and lawyers must be skillful in logical thinking and reasoning.reasoning.

Conditional StatementsConditional Statements

Also called “if then” statementsAlso called “if then” statements Used in mathematics, logical reasoning and Used in mathematics, logical reasoning and

computer programing.computer programing. Composed of 2 partsComposed of 2 parts

The “if” or hypothesisThe “if” or hypothesis The “then” or conclusionThe “then” or conclusion

Often described as: if p then q. p is the Often described as: if p then q. p is the hypothesis and q is the conclusion.hypothesis and q is the conclusion.

Alterations of the Conditional StatementAlterations of the Conditional Statement

(We can change the statements by switching the order of the hypothesis and (We can change the statements by switching the order of the hypothesis and conclusion)conclusion)

ConverseConverse: switching the hypothesis and the : switching the hypothesis and the conclusion.conclusion. If q then pIf q then p

(We can change statements by Negation: adding the word “not” to the (We can change statements by Negation: adding the word “not” to the statements)statements)

InverseInverse: negate the hypothesis and conclusion.: negate the hypothesis and conclusion. If ~p then ~qIf ~p then ~q

ContrapositiveContrapositive: negate and switch the hypothesis : negate and switch the hypothesis and conclusionand conclusion If ~q then ~pIf ~q then ~p

LiteratureLiteratureLewis Carrol, author of Alice’s Adventures in Wonderland and Through The Looking Glass, was a mathematician as well as a writer. He was a master at creating puzzles and making connections between mathematics and literature. Following is an example of some of his statements.

Babies are illogical. Nobody is despised who can manage a crocodile. Illogical persons are despised.

The conclusion I the last statement may seem confusing. Let’s rewrite each statement in “if – then” form to help us to make the progression of the logic easier to understand.

Continue Continue

STATEMENT IF- THEN FORM:

Babies are illogical If a person is a baby, then the person is illogical

Nobody is despised who can manage a crocodile.

If a person can manage a crocodile, then that person is not despised.

Illogical persons are despised

If a person is not logical, than the person is despised.

Example:Conditional StatementsExample:Conditional Statements

ConditionalConditional

If x +1 is even, then x is oddIf x +1 is even, then x is odd ConverseConverse

If x is odd, then x + 1 is evenIf x is odd, then x + 1 is even InverseInverse

If x + 1 is not even, then x is not oddIf x + 1 is not even, then x is not odd ContrapositiveContrapositive

If x is not odd, then x + 1 is not evenIf x is not odd, then x + 1 is not even

Example: Conditional Statement Example: Conditional Statement

Conditional:Conditional:If m<A = 30If m<A = 30°, then <A is acute.°, then <A is acute. Inverse:Inverse:If m<A ≠ 30°, then <A is not acuteIf m<A ≠ 30°, then <A is not acute Converse:Converse:If <A is acute, then m<A = 30°If <A is acute, then m<A = 30° Contrapositive:Contrapositive:If < A is not acute, then m<A ≠30°If < A is not acute, then m<A ≠30°

Euler’s DiagramEuler’s Diagram

If Binti is a gorilla, then she is a primateIf Binti is a gorilla, then she is a primate

• BINTI

Gorillas

Primates

Equivalent Statements:Equivalent Statements: When two statements When two statements are both true or both false. are both true or both false. A Conditional statement is equivalent to it’s A Conditional statement is equivalent to it’s

contra-positivecontra-positive Similarly, an inverse and converse of any Similarly, an inverse and converse of any

conditional statement will be equivalent.conditional statement will be equivalent.

Your turn:Your turn:

Draw a Venn Diagram ( Euler’s Diagram) . Draw a Venn Diagram ( Euler’s Diagram) . Then write the sentence in “ if-then” form.Then write the sentence in “ if-then” form.

Staff members are allowed in the faculty Staff members are allowed in the faculty lounge.lounge.

Solution:Solution:

People in the cafeteria

Staff members

If a person is a staff member, then the person is allowed in the faculty cafeteria.

POSTULATE LAND

Postulate 5Postulate 5

Through any two points there exists exactly Through any two points there exists exactly one line.one line.

A

B


A line contains at least 2 pointsA line contains at least 2 points

A

B


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


Through any three non-collinear points there Through any three non-collinear points there exists exactly one plane.exists exactly one plane.

AB

C

Postulate 9 Postulate 9

A plane contains at least three noncollinear A plane contains at least three noncollinear points.points.

AB

C


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

AB


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

http://www.icoachmath.com/SiteMap/IntersectingPlanes.html

Let’s practiceLet’s practice

Remember to study the lesson before you Remember to study the lesson before you complete your homework.complete your homework.

Geometry Section 2.1 Conditional Statements NCSCOS: (2.01; 2.02) Ms. Vasili.

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