Download If a point is equidistant from the endpoints of the segment, then it is

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If a point is on the perpendicular bisector of a segment, then it is
equidistant from the endpoints of the segment.
If a point is equidistant from the endpoints of the
segment, then it is on the perpendicular bisector.
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Types of statements:
Conditional
Converse
Biconditional
Inverse
Negation
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Evaluate the truth value of the
statement:
BellefonteisthecapitalofPennsylvania
Write the statement's negation
Negation:
Bellefonte is NOT the capital of
Pennsylvania.
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Inverse of a conditional statement
both the hypothesis and conclusion are
negated
Contrapositive of a conditional statement
hypothesis and conclusion are flipped
around AND both negated
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Conditional Statement:
If a figure is a square, then it is a rectangle.
Converse:
If a figure is a rectangle, then it is a square.
Inverse:
If a figure is not a square, then it is not a rectangle.
Contrapositive:
If a figure is not a rectangle, then it is not a square.
Evaluate the truth values of the statements
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A conditional statement and its contrapositive
are said to be equivalent statements since they
always have the same truth-value.
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Conditional:
If you don't stand for something, then you'll
fall for anything
Converse:
If you fall for anything, then you don't
stand for something.
Inverse:
If you stand for something, then you won't
fall for anything.
Contrapositive:
If you don't fall for anything, then you'll
stand for something.
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Equivalent Statements
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Proofs Using Indirect Reasoning
How to use indirect reasoning:
Prove all possibilities are FALSE except
one, that one must be TRUE
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Steps to writing an indirect proof
Step 1: Assume that the negation of what you
want to prove is true.
Step 2: Show that this assumption from step 1
leads to a contradiction (with the given)
Step 3: Conclude that your original (negated)
assumption must be false and
therefore what you want to prove is
true
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Assume that Quadrilateral QRWX DOES
have 4 acute angles.
Assume an integer n is not divisible by 5.
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w/ base angles
and
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Two angles are not congruent
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a. If a figure is not a rectangle, then it
doesn't have four sides
b. If a figure doesn't have four sides, then it
is not a rectangle.
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Assume that Triangle PEN is not isosceles
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I and II
since a right triangle can't be equilateral
I and II
since it must be a right triangle if A and C are
both 60 degrees, B can't be a right angle.
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a. 20 or more members
b. Total membership is fewer than 20
c. The Debate Club has few than 10
members.
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a. if four points are not collinear, then
they are not coplanar - FALSE - see
points above
b. if four points are not coplanar, then
they are not collinear - TRUE
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27) If a student attends school in the
Fairmont building, then she has Jon Downs
as a school director.
Inverse: If a student doesn't attend school in
the Fairmont Building, then she doesn't
have Jon Downs as a school director
s
28. Not possible. If the conditional statement
is true, the contrapositive will always have the
same truth value, so it would also have to be
true.
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