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

Lesson Opener – Conditional Statements Beagles Animals Dogs Hartford Venn Diagram

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

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

Conditional Statements Also called “if then” statements Also called “if then” statements Used in mathematics, logical reasoning and computer programing. Used in mathematics, logical reasoning and computer programing. Composed of 2 parts Composed of 2 parts The “if” or hypothesis The “if” or hypothesis The “then” or conclusion The “then” or conclusion Often described as: if p then q. p is the hypothesis and q is the conclusion. Often described as: if p then q. p is the hypothesis and q is the conclusion.

Alterations of the Conditional Statement (We can change the statements by switching the order of the hypothesis and conclusion) Converse: switching the hypothesis and the conclusion. Converse: switching the hypothesis and the conclusion. If q then p If q then p (We can change statements by Negation: adding the word “not” to the statements) Inverse: negate the hypothesis and conclusion. Inverse: negate the hypothesis and conclusion. If ~p then ~q If ~p then ~q Contrapositive: negate and switch the hypothesis and conclusion Contrapositive: negate and switch the hypothesis and conclusion If ~q then ~p If ~q then ~p

Literature Lewis 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 STATEMENTIF- THEN FORM: Babies are illogicalIf 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 Statements Conditional Conditional If x +1 is even, then x is odd Converse Converse If x is odd, then x + 1 is even Inverse Inverse If x + 1 is not even, then x is not odd Contrapositive Contrapositive If x is not odd, then x + 1 is not even

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

Euler’s Diagram If Binti is a gorilla, then she is a primate If Binti is a gorilla, then she is a primate BINTI Gorillas Primates

Equivalent Statements: When two statements are both true or both false. Equivalent Statements: When two statements are both true or both false. A Conditional statement is equivalent to it’s contra-positive A Conditional statement is equivalent to it’s contra-positive Similarly, an inverse and converse of any conditional statement will be equivalent. Similarly, an inverse and converse of any conditional statement will be equivalent.

Your turn: Draw a Venn Diagram ( Euler’s Diagram). Then write the sentence in “ if-then” form. Draw a Venn Diagram ( Euler’s Diagram). Then write the sentence in “ if-then” form. Staff members are allowed in the faculty lounge. Staff members are allowed in the faculty lounge.

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 5 Through any two points there exists exactly one line. Through any two points there exists exactly one line. A B

Postulate 6 A line contains at least 2 points A line contains at least 2 points A B

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

Postulate 8 Through any three non-collinear points there exists exactly one plane. Through any three non-collinear points there exists exactly one plane. A B C

Postulate 9 A plane contains at least three noncollinear points. A plane contains at least three noncollinear points. A B C

Postulate 10 If two points lie in a plane, then the line containing them lies in the plane. If two points lie in a plane, then the line containing them lies in the plane. A B

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

Let’s practice Remember to study the lesson before you complete your homework. Remember to study the lesson before you complete your homework.