Download 2-5: Verifying Segment Relationships

Expectation:
You will:
1.Write proofs in “If, then…” form.
2.Write the negations of “all,” “every” “no” and “there exists”
statements.
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Jerry stated that squaring a number always results in a
positive result. Is this statement true or false. If false,
provide a counterexample.
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Equivalence Property of Congruence
Theorem
a. Congruence of segments is reflexive:
b. Congruence of segments is symmetric:
c. Congruence of segments is transitive:
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Parts of a Geometric Proof
a. State the theorem (may already be done for you).
b. State the given (hypothesis) and what you are trying
to prove (conclusion).
c. Draw a diagram.
d. Start with the given and deduce statements until you
reach the conclusion (connect the given and the prove
with a logic chain).
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In order to be a good proof writer, you MUST know all of
the postulates definitions and theorems.
Take the next 15 minutes to make a complete list (not a
part of your notes) of all of our postulates definitions
and theorems up to this point. If you do not finish in
the time allotted, it is expected that you will complete
the list by class tomorrow.
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Prove the Symmetric Property of
Congruence
State the theorem:
What is the given?
What must we prove?
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Complete the Proof
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Let’s do another one together!
Given: P, Q and S are collinear
Prove: PQ = PS – QS
P
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Q
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S
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Identify the “given” and the “prove.”
The statement is not supposed to make
sense.
If a thingamabob is fluzzelled, then it has been
whompied.
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Complete the proof below by filling in the
blanks.
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Complete the Proof.
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Assignment 2-5-1
Skills Practice 2-7
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Write the negation of the following
statement.
The ball is blue.
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Write the negation of the given
statement.
Every ball is blue.
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Negating all, every and no statements.
What would we need to show to prove the following
statement is false?
“Every car is black.”
So how many non-black cars are needed for the
negation?
Write the negation of the given statement.
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Negating all, every and no statements.
What would we need to show to prove the following
statement is false?
“All cheese is orange.”
So how many non-orange cheeses are needed for the
negation?
Write the negation of the given statement.
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Negating all, every and no statements.
What would we need to show to prove the following
statement is false?
“No triangles have right angles.”
So how triangles with right angles are needed for the
negation?
Write the negation of the given statement.
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One more special type of negation.
“There exists a plane that contains A, B, C and D.”
How can we negate (make false) this statement?
Write the negation of this statement.
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What is the negation of the statement, “No squares are
triangles?”
A.all squares are triangles
B.all triangles are squares
C.no triangles are squares
D.there exists at least one square that is a triangle.
E. There exists at least one triangle that is a square.
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Now back to proofs!
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Assignment 2-5-2
pages 104-105,
# 15-31 (odds), 39-45 (odds).
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