1. To Start: 10 Points
Explain the difference between a Median of a triangle and an altitude of a triangle?

2. Chapter 5: Relationships within Triangles
Section 5.5: Indirect Proofs

3. Indirect Reasoning
In INDIRECT REASONING, all possibilities are considered then all but one are proved false. The remaining possibility must be true.
Yes???

4. Indirect Proofs
A proof involving indirect reasoning is an indirect proof.
For example: If you have two friends named Joe and while you were out your mom calls and said “Your friend Joe stopped by the house to see you”. Which Joe was it?
How many possibilities are there? Two!
Well if one of your friends named Joe is out of town for the week, then it must have been the other friend named Joe!
Therefore, you used indirect reasoning by proving the other possibilities false, so the only remaining possibility must be true!!

5. Writing an Indirect Proof
3 Steps!!!
1. Assume the opposite of what you want to prove is true.
2. Find a contradiction to prove that your assumption false.
3. Conclude that the assumption is false and therefore what you want to prove must be true.

6. Step 1of an Indirect Proof
Write the first step of an indirect proof for the following:
A. It is raining outside.
Assume it is not raining outside.
B. A number is divisible by 5.
Assume the number is not divisible by 5.
C. You don’t have swim practice today
Assume you do have swim practice today.
ASSUME the
Opposite!!!

7. Identify Contradictions
Step 2: Form a contradiction!
Which two statements contract each other?
A and C contradict each other!

8. Writing an Indirect Proof
Step 1: Assume the sidewalk surface is warmer than 32 degrees.
Step 2: If the sidewalk surface is warmer than 32 degrees, then ice would not be forming. This contradicts the given information that that ice IS forming on the side walk.
Step 3: therefore, the assumption is false and the surface of the sidewalk is 32 degrees or lower!
Ice is forming on the sidewalk in front of the school. Show that the temperature of the sidewalk surface must be 32 degrees or lower.

9. Writing an Indirect Proof
A triangle has three congruent sides. Show the triangle must be an equilateral triangle.
Step 1: Assume the triangle is not equilateral.
Step 2: If the triangle is not equilateral, then the three sides are not congruent. This contradicts the given information that the triangle has three congruent sides.
Step 3: Therefore, the assumption is false and the triangle must be an equilateral triangle.

10. Homework!!!
Page 319
1-2, 3-15, 18-21, 24
5.5 Worksheet