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Transcript
Conditionals, Biconditionals, and Deductive
Reasoning and algebraic properties


Be able to write a converse of a conditional
statement (Geometry and Spatial Sense, GR9,1)
Be able to write a biconditional
(Geometry and Spatial Sense, GR9,1)

Use law of detachment and law of
syllogism to draw conclusions
(Geometry and Spatial Sense, GR9,1)

Use algebraic properties to prove a
statement (Geometry and spatial sense, GR9, 1)
Lets begin with an OGT question….
The graph as shown represents the amount of money Sarah can earn at
her part-time job
Which of the following equations best represents the relationship
between Sarah’s pay and the hours she works?
A. y = 4x
B. y = 6.5x
C. y = 4x + 10
D. y = 6.5x + 10

If-Then Statements

Hypothesis – If statement

Conclusion – Then statement

Identify the Hypothesis and Conclusion:
◦ If two lines are parallel, then they are coplanar

Identify the Hypothesis and Conclusion:
◦ If two lines are parallel, then they are coplanar
◦ Hypothesis: Two lines are parallel
◦ Conclusion: They are coplanar

Write the statement as a conditional
◦ An acute angle measures less than 90º

Identify the Hypothesis and Conclusion:
◦ If two lines are parallel, then they are coplanar
◦ Hypothesis: Two lines are parallel
◦ Conclusion: They are coplanar

Write the statement as a conditional
◦ An acute angle measures less than 90º
◦ If an angle is acute, then it measures less than 90
Converse
The converse
converse of
of aaconditional
conditional statement
if
•  The
statement is
formed by exchanging the hypothesis and the
formed
by in
switching
the hypothesis and the
conclusion
the conditional.
conclusion
Example
3: in the conditional.
◦ Conditional- If a figure is a triangle, then it has three
– angles.
Conditional- If a figure is a triangle, then it has
three angles.
◦ Converse- If a figure has three angles, then it is a
triangle.
– Converse- If a figure has three angles, then it is a
triangle.

If x = 5, then x + 15 = 20
◦ Write the converse:

If x = 5, then x + 15 = 20
◦ Write the converse:
◦ If x + 15 = 20, then x = 5
◦ Write the Biconditional:

If x = 5, then x + 15 = 20
◦ Write the converse:
◦ If x + 15 = 20, then x = 5
◦ Write the Biconditional:
◦ X = 5 if and only if x + 15 = 20

Write two statements that form this
biconditional:
◦ Lines are skew if and only if they are noncoplanar

Write two statements that form this
biconditional:
◦ Lines are skew if and only if they are noncoplanar
◦ If lines are skew, then they are noncoplanar
◦ If lines are noncoplanar, then they are skew



If a conditional is true and its hypothesis is
true – then its conclusion is true
If p implies q is true and p is true then q is
true
Can you make a conclusion?…
◦ Every High School student likes music.
◦ Ling likes music



If a conditional is true and its hypothesis is
true – then its conclusion is true
If p implies q is true and p is true then q is
true
Can you make a conclusion?…
◦ Every High School student likes music. Ling likes
music
◦ If you are a high school student, then you like
music
If p implies q is true and q implies r is true,
then p implies r is true
P Q and QR, then PR


If a quadrilateral is a square, then it contains
4 right angles.
If a quadrilateral contains 4 right angles, then
it is a rectangle

A gardener knows that if it rains, the garden
will be watered.
It is raining.


If you want to build a skyscraper, start with a
good foundation. The foundation is a
concrete form that supports the rest of the
structure.
The foundation of geometry is made of
statements called postulates. These are
accepted as true.

Addition Property

Subtraction Property

Multiplication Property

Division Property

Reflexive Property

Symmetric Property

Transitive Property

Substitution Property

Distributive Property

Fill in…
3x
2x + 1
AB + BC = AC
3x + 2x + 1 = 36
5x + 1 = 36
5x = 35
X=
Simplify
AC = 36
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