Download Unit 2.2

UNIT 2: REASONING AND PROOF
2.2 - Biconditional Statements
Biconditional Statements
Vocabulary
Perpendicular Lines
Line Perpendicular
to a Plane
Definitions
MA30: GEOMETRY
(Text Ref: Ch 2.2 Pg 79-85)
I. Biconditional Statements
A. Vocabulary
Biconditional Statement –
Perpendicular Lines –
Line Perpendicular to a Plane –
Definitions –
B. Writing a Biconditional Statement
1) Rewrite the definition of a Perpendicular Line as an
If - Then statement.
Writing a
Biconditional Statement
a)
b)
2) Rewrite the definition of a Perpendicular Line as a
Biconditional Statement
Rewriting a
Biconditional Statement
C. Rewriting a Biconditional Statement
1) Rewrite the biconditional statement as a conditional
statement and its converse.
a) An angle is a right angle iff its measure is 90.
Conditional Statement -
Converse b) A number is even if and only if it is divisible by two.
Conditional Statement -
Converse -
c) A point on a segment is the midpoint of the segment
if and only if it bisects the segment.
Conditional Statement -
Converse -
2.2 – Biconditional Statements (continued)
Analyzing
Biconditional Statments
D. Analyzing a Biconditional Statement
Consider the following statement.
a) Is this a biconditional statement?
b) Is the statement true?
1) “You attend school if and only if it is a weekday.”
2) “It rains iff there are clouds in the sky.”
3) Two angles are adjacent angles if and only if they share a
vertex and one side but do not have any common interior
points.
E. Writing a Biconditional Statement
Each statement is true.
a) Write the converse of the statement and decide whether
the converse is true or false.
b) If the converse is true, conbine it with the original statement
to form a true biconditional statement.
c) If the converse is false, state a counterexample.
Writing a
Biconditional Statement
1) If the product ab is negative, then either a is negative or
b is negative.
2) If the sides of two angles form two pairs of opposite rays,
then the angles are vertical angles.
3) If the product ab is 0, then either a must be 0 or b
must be zero.