Understanding Biconditional Statements in Geometry: Conditional, Converse, and Writing, Exams of Geometry

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2.2 Definitions and

Biconditional

Statements

Geometry Mr. Peebles 03/20/

Geometry Bell Ringer

Write the Contrapositive of the

following conditional statement:

If the polygon has three sides, then

it’s a triangle.

Standard/Objectives

Daily Learning Target (DLT)

Wednesday March 20, 2013

“I can recognize, use, and write

biconditional statements in real

life.”

Assignment Due Today:

• Pp. 83-

(1-17 Odds, 31, 37, 39, 54-58, 64-66)

Example 1

 The biconditional statement below can be rewritten as a

conditional statement and its converse.

 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.

Hint: Are the conditional and converse statements true?

If so, write the biconditional.

Example 1

 The biconditional statement below can be rewritten as a

conditional statement and its converse.

 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.

 Answer: Three lines are coplanar if and only if they

lie in the same plane.

Example 2: Analyzing

Biconditional Statements

• Consider the following statement: x = 3 if and only if x^2 = 9.
• Is this a biconditional statement?
  • The statement is biconditional because it contains the phrase “if and only if.”
• Is the statement true?
  • Conditional statement: If x = 3, then x^2 = 9.
  • Converse: x^2 = 9, then x = 3.
    • The first part of the statement is true, but what about -3? That makes the second part of the statement false.

Example 3: Writing a

Biconditional Statement

• Each of the following is true. Write the

converse if each statement and decide whether

the converse is true or false. If the converse is

TRUE, then combine it with the original

statement to form a true biconditional

statement. If the statement is FALSE, then

state a counterexample.

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

Example 4: Writing a

Biconditional Statement

• Conditional: If a number ends in 0, then the number is divisible by 5.
• Converse: If a number is divisible by 5; then the number ends in 0.

Can you write a biconditional statement from the information given from the conditional and converse statements?

Example 4: Writing a

Biconditional Statement

• Conditional: If a number ends in 0, then the number is divisible by 5.
• Converse: If a number is divisible by 5; then the number ends in 0.
• The converse isn’t true. What about 25?
• Knowing how to use true biconditional statements is an important tool for reasoning in Geometry. For instance, if you can write a true biconditional statement, then you can use the conditional statement or the converse to justify an argument.

Example 5: Writing a Postulate as a Biconditional Statement

• Answer: Point B lies between points A

and C if and only if AB + BC = AC.

Assignment:

• pp. 90-92 (1-6 and 38-40)