October 06, 2011
Section 2.3 : Definitions and Biconditionals
All animals that live in the Everglades live in Florida.
Rewrite this in if-then form as a conditional:
If an animal lives in the Everglades, then it lives in Florida.
Was the converse of the statement? Is it true or false?
If an animal lives in Florida, then it lives in the Everglades.
The conditional is true but the converse is false!
If a polygon has 3 sides,
then the polygon is a triangle.
True or false?
What is the converse?
True or false?
October 06, 2011
When a conditional and its converse are both
true, a new statement can be created called a
biconditional.
p if and only if q
A polygon has 3 sides if and only if it is a triangle.
All right angles have a measure of 90º.
a) Rewrite the statement as a conditional.
Is it true?
b) Write the converse. Is the converse true?
c) Write the biconditional.
October 06, 2011
Definitions in geometry can be written as a
biconditional.
If a polygon is an equilateral triangle,
then the polygon has 3 congruent angles.
True or False?
Converse true or false?
October 06, 2011
Adjacent angles are angles in a plane that
have their vertices and one side in common
but no common interior points.
Definitions
biconditional.
Adjacent angles
have their
but no common in
1
•
2
Are the angles adjacent?
A
D
1 2
C
B
∠1 and ∠2
∠ABC and ∠ABD
2
2
1
3
∠1 and ∠2
∠2 and ∠3
∠1 and ∠3
2
1
1
∠1 and ∠2
∠1 and ∠2
c.) Adjacent angles are angles
1. in a plane
2. same vertex
3. one common side
4. don't overlap
October 06, 2011
1) Share a vertex
2) Share a side
3) Don't overlap