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Biconditional Statements
th
Monday
August
19
and Definitions
Logic and Conditional Statements
Modules 1-4 and 2-1
p. 29 and p. 46 in your book
Holt
Geometry
Holt
McDougal
Geometry
Biconditional Statements
and Definitions
Vocabulary
Conditional Statement – “If…then”,
,
contains a hypothesis and conclusion
Ex: If two angles are vertical angles,
then they are congruent
Holt McDougal Geometry
Biconditional Statements
and Definitions
Converse – interchange (flip) the hypothesis
and conclusion
If 2 angles are congruent, then they are vertical
angles
Inverse – Negate both hypothesis and
conclusion
If two angles are NOT vertical angles, then they
are NOT congruent
Contrapositive – Interchange & negate
both hypothesis and conclusion
If 2 angles are NOT congruent, then they are
NOT vertical angles
Holt McDougal Geometry
Biconditional Statements
and Definitions
True or False
Conditional Statement – If 2 angles are
vertical angles, then they are congruent
Converse –If 2 angles are congruent, then they
are vertical angles
Inverse –If two angles are NOT vertical angles,
then they are NOT congruent
Contrapositive – If 2 angles are NOT
congruent, then they are NOT vertical angles
Holt McDougal Geometry
Biconditional Statements
and Definitions
On your own…
Complete the statements for letters
a – f and label each statement
as “T” or “F”
Holt McDougal Geometry
Biconditional Statements
and Definitions
A) If I receive a scholarship,
then I will go to college
• CONVERSE If I go to college, then I
received a scholarship (FALSE)
• INVERSE If I don’t get a scholarship, then
I won’t go to college (FALSE)
• CONTRAPOSITVE If I didn’t go to college,
then I didn’t receive a scholarship (FALSE)
Holt McDougal Geometry
Biconditional Statements
and Definitions
B) If a squares side is 5cm, then
its area is 25cm2
• CONVERSE If a squares area is
25cm2, then its side is 5cm (TRUE)
• INVERSE If a squares side is NOT
5cm, then its area is NOT 25cm2
(TRUE)
• CONTRAPOSITVE If a squares area
is NOT 25cm2, then its side is NOT
5cm (TRUE)
Holt McDougal Geometry
Biconditional Statements
and Definitions
C) If they run a marathon, then
they will feel exhausted
• CONVERSE If they feel exhausted, then
they ran a marathon (FALSE)
• INVERSE If they don’t run a marathon,
then they won’t feel exhausted (FALSE)
• CONTRAPOSITVE If they don’t feel
exhausted, then they didn’t run a
marathon (TRUE)
Holt McDougal Geometry
Biconditional Statements
and Definitions
D) If a figure is reflected, then
its orientation changes.
• CONVERSE If the orientation
changes, then the figure was reflected
(FALSE)
• INVERSE If the figure isn’t reflected,
then its orientation doesn’t change
(FALSE)
• CONTRAPOSITVE If a figures
orientation doesn’t change, then the
figure wasn’t reflected (TRUE)
Holt McDougal Geometry
Biconditional Statements
and Definitions
E) If a quadrilateral is a
rhombus, then its an equilateral
• CONVERSE If a quad is equilateral,
then it’s a rhombus(FALSE)
• INVERSE If a quad is not a
rhombus, then its not
equilateral(FALSE)
• CONTRAPOSITVE If a quad is not
equilateral, then its not a rhombus
(TRUE)
Holt McDougal Geometry
Biconditional Statements
and Definitions
F) If a triangle is isosceles, then
it is also equilateral
• CONVERSE If a triangle is
equilateral, then its isosceles(FALSE)
• INVERSE If a triangle is not
isosceles, then its not equilateral
(FALSE)
• CONTRAPOSITVE If a triangle is not
equilateral, then its not isosceles
(TRUE)
Holt McDougal Geometry
Biconditional Statements
th
Tuesday
August
20
and Definitions
Logic and Conditional Statements
Modules 1-4 and 2-1
p. 29 and p. 46 in your book
Holt
Geometry
Holt
McDougal
Geometry
Biconditional Statements
and Definitions
Holt McDougal Geometry
Biconditional Statements
and Definitions
• If a conditional statement is true, then its
converse is
true
• If a conditional statement is true, then its
inverse is
true
• If a conditional statement is true, then its
contrapositive is
true
Holt McDougal Geometry
Biconditional Statements
and Definitions
Biconditional Statement – When a
conditional statement, its converse,
inverse and contrapositive are all
true. We can use the phrase “if and
only if” (iff) or the symbol
Holt McDougal Geometry
Biconditional Statements
and Definitions
• Ex: A pentagon is a five-sided polygon
• Converse – If a figure is a five-sided
polygon, then it’s a pentagon
• Inverse – If a figure is NOT a pentagon,
then its NOT five-sided polygon
• Contrapositive – If a figure is NOT a fivesided polygon, then its NOT a pentagon
• Biconditional – A figure is a pentagon if
and only if it’s a five-sided polygon
Holt McDougal Geometry
Biconditional Statements
and Definitions
On your own…
Complete #’s 4 and 5 on the worksheet
Holt McDougal Geometry
Biconditional Statements
and Definitions
4)
• The only statement that is a biconditional
is letter b) If a square’s side is 5cm, then
its area is 25cm2
• A square’s side is 5cm if and only if its
area is 25cm2
Holt McDougal Geometry
Biconditional Statements
and Definitions
5)
• Biconditional Statement Examples…
• A figure is a triangle if and only if it’s a
polygon with three sides
• An angle is a right angle if and only if it’s
measure is exactly 900
Holt McDougal Geometry