Transcript 6-3 Indirect Proof

Geometry Warm ups
What
is ___
the relationship between the lengths of
___
RS and ST?
What is the___
relationship
between the
___
lengths of RT and ST?
What is the relationship between the measures of
<A and <B? **Look at whiteboard
What is the relationship between the measures of
<B and <C? **Look at whiteboard
5) Write the sentence that helps you remember the
special segments
5-4 Indirect Proof
Indirect Proof
1. Assume temporarily that opposite of prove.
2. Then think how to contradict the info.
3. But this contradicts Given.
4. Therefore the temporary assumption that
opposite of prove must be false.
5. It follows that Prove.
Ways to remember…
Always (Assume)
Take (Then)
Bread (But)
To (Therefore)
Italy (In conclusion)
The bread in Italy is not good.
Ways to remember what goes in the
blanks…
Olives (opp. Of prove)
Taste (Think)
Good/Gross (Given)
On (Opp. Prove)
Pizza (Prove)
Example
State the assumption you would make to start an
indirect proof for the statement
is not a
perpendicular bisector.
Answer: Assume temporarily that
bisector.
is a perpendicular
Example
State the assumption you would make to start an
indirect proof for the statement 3x = 4y + 1.
Answer: Assume temp. that 3x ≠ 4y + 1
TOO
A.
B.
C.
D.
TOO
A.
B.
C.
D.
Starting with If, Then
If they start with and If-Then—
The “If” part is the GIVEN
Then “Then” part is the PROVE
EXAMPLE 1
Given: In parallelogram XYZW, mX = 80°
Prove: Parallelogram XYZW is not a rectangle.
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Assume temporarily that Parallelogram XYZW is a
rectangle.
Then rectangles have all right angles which means
mX = 90°.
But this contradicts the given information that
mX = 80°.
Therefore the temporary assumption that
Parallelogram XYZW is a rectangle is false.
It follows that Parallelogram XYZW is not a
rectangle.
TOO
Given: mX ≠ mY
Prove: X and Y are not both right angles
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Assume temporarily that X and Y are both right
angles.
Then mX = 90° and mY = 90°. OR Then mX =
mY.
But this contradicts the given information
mX ≠ mY.
Therefore the temporary assumption that X and Y
are both right angles is false.
It follows that X and Y are not both right angles.
5) Write a FULL Indirect Proof
Given: 2r + 3 ≠ 17
Prove: r ≠ 7
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Assume temporarily that r = 7.
Then 2r + 3 = 2(7) + 3 = 14 + 3 = 17.
But this contradicts the given information
2r + 3 ≠ 17.
Therefore the temporary assumption that
r = 7 is false.
It follows that r ≠ 7.
HW
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Pg. 359 #11-18, 27, 28 All
WBs—I’m calling on randoms,
winners get a prize!!!
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Write ONLY the 1st sentence in the proof
1. P: ∆ABC is equilateral.
Answer: Assume temporarily that ∆ABC is not
equilateral.
2. P: a > b
Answer: Assume temporarily that a < b.
3. If a – b = 0, then a = b.
Answer: Assume temp. than a not equal to b.