regarding triangle congruence.” a valid explanation of one, but does not say it as a true conditional, then inform students that all postulates and theorems can be written as TRUE conditional statements. How can we write SSS as a true conditional statement? What do we need for a conditional statement? Exit Slip “The exit slip is a way for us to know how well we taught this lesson. It looks similar to your worksheet, but this time you will fill in all the parts. Be sure to use a math example.” On worksheet: Directions. Fill in the blanks for each conditional statement. (4 mins)
If you are a twin, then you have a sibling. If you have a sibling, then you are a twin. If I am breathing, then I am sleeping. If I am sleeping, then I am breathing. 1 a. With your partner, create a definition of a conditional statement in your own words. Create your own conditional statement. c. Challenge! (yes, you have to try this.) Write a statement that is NOT a conditional statement. When you have written your definition, write it on the board. Come to a consensus – an “if,” “then” statement. _______________________________________________________________________________________ Notes: Term Definition Example Conditional An if….then…. statement If p, then q Label hypothesis and conclusion p q (ASSUME THE HYPOTHESIS IS TRUE) Have a student share their example from Converse Feet switching back and forth Switch the p and q q p Have a student say the converse of the class example Bi-conditional Combine two statements with the same truth value using “if and only if” p q You live in Alaska if and only if you live in the largest state. Introduce converse and fill in chart. 2. a. Write the converse of your statement from question 2a. b. Is a converse a conditional statement? Why or why not? 3. a. Which conditional and converse pairs from the game were both true?
Converse: If _______________________________, then_____________________________ Could these statements be re-written as a bi-conditional? (Circle YES or NO.) 3. True or False? Counterexample? Original Statement If a triangle has three congruent sides, then the triangle is equilateral. Converse: Could these statements be re-written as a bi-conditional? (Circle YES or NO.) 4. True or False? Counterexample? Original Statement If a quadrilateral has sides of equal length, then the quadrilateral is a square. Converse: Could these statements be re-written as a bi-conditional? (Circle YES or NO.) 5. True or False? Counterexample? Original Statement If two triangles are congruent, then the areas of the two triangles are equal. Converse: Could these statements be re-written as a bi-conditional? (Circle YES or NO.) 6. True or False? Counterexample?
DIRECTIONS. For each conditional statement, complete the following: Write the converse statement. Decide if each statement is true or false. If the statement is false, provide a counterexample. 1. True or False? Counterexample? Original Statement If a number is divisible by 3, then it is odd. Converse: If ________________________________, then____________________________. 2. True or False? Counterexample? Original Statement If a triangle has a 90 degree angle, then it is a right triangle. Converse: If ________________________________, then____________________________. Are these statements bi-conditional? (Circle YES or NO.) 3. True or False? Counterexample? Original Statement If a triangle has three congruent angles, then the triangle is equilateral. Converse: Are these statements bi-conditional? (Circle YES or NO.)