Unit 2-2: Conditional Statements Mr. Schaab’s Geometry Class Our Lady of Providence Jr.-Sr. High School 2015-2016.

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Presentation transcript:

Unit 2-2: Conditional Statements Mr. Schaab’s Geometry Class Our Lady of Providence Jr.-Sr. High School

 Conditional statement – a logical statement that has a hypothesis and a conclusion.  Conditional statements can always be written in “if- then” form: Conditional Statements A student who shows their work on assignments is Mr. Schaab’s favorite student. If you show your work on assignments, then you are Mr. Schaab’s favorite student. Conclusion Hypothesis

 Converse – Switch the hypothesis and conclusion:  If you’re Mr. Schaab’s favorite student, you show your work on assignments.  Inverse – Negate both the hypothesis and conclusion:  If you don’t show your work on assignments, you’re not Mr. Schaab’s favorite student.  Contrapositive – Switch and negate the hypothesis and conclusion (Converse, then Inverse):  If you’re not Mr. Schaab’s favorite student, you don’t show your work on assignments. Related Forms of Conditionals If you show your work on assignments, you’re Mr. Schaab’s favorite student.

Basketball players are athletes.  Rewrite this statement in if-then form, and write the converse, the inverse, and the contrapositive. Determine which statements are true and which are false.  If one plays basketball, one is an athlete.  If one is an athlete, one plays basketball.  If one does not play basketball, one is not an athlete.  If one is not an athlete, one does not play basketball. Conditional Statements

 Write the converse, the inverse, and the contrapositive. Determine which statements are true and which are false.  If 5x – 3 = 17, then x = 4.  If x ≠ 4, then 5x – 3 ≠ 17.  If 5x – 3 ≠ 17, then x ≠ 4. If x = 4, then 5x – 3 = 17.

Conditional Statements  Write your own conditional statement! Be prepared to share it with the class. (keep it “classy.”)

 When a conditional statement and its converse are both true, you can write them as a single statement by using the phrase “if and only if” :  Conditional: If two lines are perpendicular, then they intersect to form a right angle.  Converse: If two lines intersect to form a right angle, then they are perpendicular.  Bi-conditional: Two lines are perpendicular if and only if they intersect to form a right angle. Bi-conditional Statements

 State the following definitions as bi-conditional statements:  Collinear points are points that lie on the same line.  Points are collinear if and only if they lie on the same line.  If all three sides of a triangle are the same length, then it is an equilateral triangle.  A triangle is equilateral if and only if all three sides of the triangle are the same length.  Mr. Schaab’s room number at PHS is 312.  A room at PHS is Mr. Schaab’s room if and only if the room number is 312. Bi-conditional Statements

 Listed on iTeach as:  “2-2 HW: A-Block Due Mon. 9/15, B-Block Due Tues. 9/16 – Conditional Statements”  Do all problems  Assignment WILL be spot checked. Homework