1. Pearson Unit 1 Topic 2: Reasoning and Proof 2-3: Biconditionals and Definitions Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007

2. TEKS Focus:
(4)(B) Identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse.
(1)(F) Analyze mathematical relationships to connect and communicate mathematical ideas.

3. When you combine a conditional statement and its converse, you create a Biconditional
Statement. This statement can be written in the form “p if and only if q.” This means
“if p, then q” and “if q, then p.”
Symbolically this is written as
p q means p q and q p.
In geometry, biconditional statements are used to write definitions.

4. BICONDITIONAL BICONDITIONAL p q definition reversible
Single true statement
BICONDITIONAL
p q
has two
parts
true
conditional
true
converse

5. Biconditional Statements

7. If an animal is an insect, then __________
_______________________________________
________________________________________
it has six legs and three body parts.

8. Converse:
Biconditional:
If they are congruent, then two angles have equal measure.
Two angles are congruent if and only if they have equal measure.

9. two numbers are reciprocals, their product is 1.
Condtional 1:
If ____________________________________________________________ then
__________________________________________________________________
Condtional 2:
two numbers are reciprocals,
their product is 1.
their product is 1,
two numbers are reciprocals.

10. Example: 2 ½ : Write each definition as a biconditional.
A. A triangle is a three sided polygon.
A polygon is a triangle if and only if it has three sides.
B. Parallel lines are two coplanar lines that never intersect.
Two coplanar lines are parallel if and only if they never intersect.
C. Four coplanar points lie in the same plane.
Four points are coplanar if and only if they lie in the same plane.

11. Condtional 1:
If ____________________________________________________________, then
__________________________________________________________________
Condtional 2:
Biconditional: ___________________________________________________
___________________________________________________________________
an angle is a straight angle
the angle measures 180.
an angle measures 180
the angle is a straight angle.
An angle is a straight angle if and only if the angle
measures 180.

12. Example 4:
3 if and

13. Example 5: If you live in Austin, then you live in Texas.
You live in Austin if and only if you live in Texas.
If you live in Austin, then you live in Texas.
If you live in Texas, then you live in Austin.
The biconditional is FALSE.
TRUE
FALSE

14. Example 6: D

15. Example 7:
Is the following a good definition. If not, rewrite so that it is.
A square is a figure with four right angles.
A quadrilateral is a square if and only if it has four right angles and four congruent sides.