identifying whether a statement is TRUE or FALSE
5.
Write the converse, inverse, contrapositive, and biconditional (if possible).
Conditional:
Truth Value: _______
If a polygon has three sides, then it is a triangle.
Converse:
Truth Value ________
_____________________________________________________________
_____________________________________________________________
Inverse:
Truth Value ________
_____________________________________________________________
_____________________________________________________________
Contrapositive:
Truth Value ________
_____________________________________________________________
_____________________________________________________________
Biconditional:
Truth Value ________
_____________________________________________________________

U2 - 5
_____________________________________________________________
If a triangle has three
࠵?࠵?°
angles, then it is an equilateral triangle.
What is the
truth value
?
_________
Is there a
counterexample
? If so, what is it? ______________________
Now write the
converse
of the conditional statement and determine its
truth value
.
__________________________________________________________________
__________________________________________________________
A
biconditional statement
can ONLY be written if the __________________ and
_______________ are TRUE.
If a triangle is a right triangle, then it contains one 90° angle.
True or False? ________
Converse:
____________________________________________________________
True or False? ________
Biconditional statement
(if applicable)
__________________________________________________________________
__________________________________________________________
*Biconditional statements are important because we will use them to discuss theorems.

U2 - 6
Lesson 2.3:
Deductive Reasoning and Proofs (TB 2.4-5)
Deductive Reasoning
:
the process of reasoning that uses FACTS to form a conclusion
Postulate
:
“rule” of geometry that is accepted as true, but has NOT been proven
A
theorem
, unlike a postulate, is a statement that must be __________________
to be true.
A
proof
is a ________________________________ argument that shows that
a statement is __________________.
Two-column proof
: lists
statements
and
reasons
starting with given information and
each step that leads to the conclusion in a two column format
Paragraph proof
: gives
statements
and
reasons
in sentence format that create a
paragraph
Properties of Equality
Property
How It Works
Addition Property of Equality
If
࠵? = ࠵?
, then
࠵? + ࠵? = ࠵? + ࠵?
.
Subtraction Property of Equality
If
࠵? = ࠵?
, then
࠵? − ࠵? = ࠵? − ࠵?
.
Multiplication Property of Equality
If
࠵? = ࠵?
, then
࠵?࠵? = ࠵?࠵?
.
Division Property of Equality
If
࠵? = ࠵?
, then
0
1
=
2
1
where
࠵? ≠ 0
.
Substitution Property
If
࠵? = ࠵?
, then
࠵?
can be substituted for
࠵?
in any equation containing
࠵?
.
Distributive Property
࠵?(࠵? + ࠵?) = ࠵?࠵? + ࠵?࠵?
Reflexive Property of Equality
࠵? = ࠵?
Symmetric Property of Equality
If
࠵? = ࠵?
, then
࠵? = ࠵?
.
Transitive Property of Equality
If
࠵? = ࠵?
and
࠵? = ࠵?
, then
࠵? = ࠵?
.
** These properties of equality will be used in both
algebraic
and
geometric
proofs. **

U2 - 7
(There are also Reflexive, Symmetric, and Transitive Properties of
Congruence
so be very specific when stating which one you want to use!!)
Properties of Congruence
Property
Example:
Congruence of
Segments
Example:
Congruence of
Angles
Reflexive Property
of Congruence
࠵?࠵?
≅ ࠵?࠵?
∠࠵? ≅ ∠࠵?
Symmetric Property
of Congruence
If
࠵?࠵?
≅ ࠵?࠵?
,
then
࠵?࠵?
≅ ࠵?࠵?
.
If
∠࠵? ≅ ∠࠵?
,
then
∠࠵? ≅ ∠࠵?
.
Transitive Property
of Congruence
If
࠵?࠵?
≅ ࠵?࠵?
and
࠵?࠵?
≅ ࠵?࠵?
,
then
࠵?࠵?
≅ ࠵?࠵?
.

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- Spring '14
- Logic, Transitive Property, symmetric property, Property of Equality, Reflexive Property