Warm Up

€

27x 5y 4

9

64y−2

y 4

200w−3x−5

x−3

1. If I get all of my homework done, then I will go to the game.

2. If Bert goes shopping for groceries, then it’s Wednesday.

3. If the # is two, then it is a factor of every even number.

4. False |-9+6| does not equal to |-9|+|6|

5. True

6. false

7. Converse: If you like to be at the beach, then you like volleyball. False

Inverse: If you don’t like volleyball, then you don’t like the beach. False

Contrapositive: If you don’t like to be at the beach, then you don’t like volleyball. False

8. Converse: If x is odd, then x+1 is even. True

Inverse: If x+1 is not even, then x is not odd. True

Contrapositive: If x is not odd, then x+1 is not even. True.

• Postulate 5: Through any two points there exists one line.

• Postulate 6: A line contains at least two points.• Postulate 7: If two lines intersect, then their

intersection is exactly one point.• Postulate 8: Through any three noncollinear

points there exists exactly one plane.• Postulate 9: A plane contains at least three

noncollinear points.• Postulate 10: If two points lie in a plane, then

the line containing them lies in the plane.• Postulate 11: If two planes intersect, then their

intersection is a line.

Lesson 2.2: Biconditional Statements

•Students will analyze and rewrite conditional and biconditional statements.

•Students will write the inverse, converse, and contrapositive of a conditional statement.

Examples of Conditional: It is Saturday, only if I am working at the

restaurant.

If-then form:If it is Saturday, then I am working at the

restaurant.Biconditional Statement: a statement that

contains the phrase “if and only if.” Writing a biconditional statement is equivalent to writing a conditional statement and its converse.

How do I form a biconditional statement?

Conditional Statement: If three lines are coplanar, then they lie in the same plane.

Converse: If three lines lie in the same plane, then they are coplanar.

A biconditional statement can be either true or false. To be true, both the conditional statement and its converse must be true.

Must be true “forwards” and “backwards”

Analyze the following statements to determine if they are biconditional statements:

Two angles are complementary if and only if (iff) their sum is 900.

a. Is this biconditional statement?Yes

b. Is the statement true?– Conditional Statement: If two angles are complementary, then their sum is 900.– Converse: If the sum of two angles is 900, then the angles are

complementary.

The following statement is true. Write the converse and decide whether it is true or false.

If the converse is true, combine it with the original to form a biconditional.

• If x2=4, then x=2 or -2

• Converse:

If x=2 or -2, then x2=4; true

• Biconditional:

x2=4 if and only if (iff) x=2 or -2