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5.6 Inequalities in 2 Triangles and 5.4 Indirect Proof.notebook
1
November 19, 2013
"Do Now"Let's pretend you are a head football
coach.Your team has possession of the ball.
It's 4th and 7 from your own 5 yard line.
Would you rather..
a) Go for itb) Punt the football
You need to pick a or b and be prepared to explain your reasoning.
5.6 Inequalities in 2 Triangles and 5.4 Indirect Proof.notebook
2
November 19, 2013
http://www.grantland.com/story/_/id/9970245/grantlandchannelcoachneverpunts
Math shows on 4th Down: Go for it
The Coach who never punts and always onside kicks
5.6 Inequalities in 2 Triangles and 5.4 Indirect Proof.notebook
3
November 19, 2013
Review Last Class
If a side is longer than another side, what does that mean about the angles opposite the sides?
If an angle is greater than another angle, what does that mean about the sides opposite the angles?
The Triangle Inequality Theorem states ...
5.6 Inequalities in 2 Triangles and 5.4 Indirect Proof.notebook
4
November 19, 2013
The lengths of two sides of a triangle are given.Describe the lengths possible for the third side.
8, 12
5, 16
6, 6
5.6 Inequalities in 2 Triangles and 5.4 Indirect Proof.notebook
8
November 19, 2013
Hinge Theorem
Unit 6: Relationships in Triangles5.6 Inequalities in 2 Triangles
Date
If: two sides of one are congruent to two sides of another and the included angle of the 1st is greater than the included angle of the 2nd
Then: the 3rd side of the 1st is longer than the 3rd side of the 2nd .
5.6 Inequalities in 2 Triangles and 5.4 Indirect Proof.notebook
9
November 19, 2013
Converse of Hinge
Theorem
If: two sides of one are congruent to two sides of another and the 3rd side of the 1st is longer than the 3rd side of the 2nd
Then: the included angle of the 1st is greater than the included angle of the 2nd .
5.6 Inequalities in 2 Triangles and 5.4 Indirect Proof.notebook
11
November 19, 2013
Breaking: Ms. Stalvey's coffee mug went missing
We want to prove Annette didn't take it
How can we prove that?(Especially since it's negative)
5.6 Inequalities in 2 Triangles and 5.4 Indirect Proof.notebook
12
November 19, 2013
Let's try this:Let's assume Annette did take it
If we can show this to be false,then the negative of that statement(Annette didn't steal it) will be true
5.6 Inequalities in 2 Triangles and 5.4 Indirect Proof.notebook
13
November 19, 2013
Suppose Annette took the mug.
If she took the mug, then she took it when Ms. Stalvey wasn't in the room.
If she took in when Ms. Stalvey wasn't in the room, then it was during Ms. Stalvey's planning period.
If she took it during Ms. Stalvey's planning period, then Annette wasn't in science class.
But, Annette was in science class.
Therefore, Annette didn't take Ms. Stalvey's mug.
5.6 Inequalities in 2 Triangles and 5.4 Indirect Proof.notebook
14
November 19, 2013
Indirect Proof(Proof by Contradiction)
Another proof method
1. Assume temporarily that the conclusion(what you're trying to prove) isn't true
2. Reason logically until you reach a contradiction of a known fact, theorem, definition, etc.
3. Then, it follows that the temporary assumption is false and the conclusion must be true.
Note: Leave Given info alone only negate the conclusion
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