Answers to Homework
12)a) She assigns hours of homework b) No Conclusion
c) He is not a math teacher
d) No Conclusion
14)a) Stu loves Geometry
b) No Conclusion
c) No Conclusion
d) George is not my student
16)a) JL ┴ KM
b) No Conclusion
c) No Conclusion
d) NOPQ is not a rhombus
18)a) No Conclusion
b) Last is not a rhombus or a square
c) PQRS is a rhombus
d) No Conclusion
6-3 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 (Given)
On (Opp. Prove)
Pizza (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°. Using
substitution, 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.
Multiple Choice
Theorem: A triangle has at most one obtuse angle.
Eduardo is proving the theorem above by contradiction. He
began by assuming that in  A B C <A and <B are both
obtuse. Which theorem will Eduardo use to reach a
contradiction?
A) If two angles of a triangle are equal, the sides opposite those
angles are equal.
B) If two supplementary angles are equal, the angles each
measure 90°.
C) The largest angle in a triangle is opposite the longest side.
D) The sum of the measures of the angles of a triangle is 180°.
ANSWER: D
Starting with If, Then
If they start with and If-Then—
The “If” part is the GIVEN
Then “Then” part is the PROVE
Try On Own (On WBs)
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Pg 215 #2-5 (only first sentence)
Answers:
2. Assume temporarily that ∆ABC is not equilateral.
3. Assume temporarily that Doug is not Canadian.
4. Assume temporarily that a < b.
5. Assume temporarily that Kim is a violinist.
Homework
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Pg. 216 #1-10