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

5

November 19, 2013

5.6 ­ Inequalities in 2 Triangles and 5.4 ­ Indirect Proof.notebook

6

November 19, 2013

5.6 ­ Inequalities in 2 Triangles and 5.4 ­ Indirect Proof.notebook

7

November 19, 2013

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

10

November 19, 2013

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

5.6 ­ Inequalities in 2 Triangles and 5.4 ­ Indirect Proof.notebook

15

November 19, 2013

5.6 ­ Inequalities in 2 Triangles and 5.4 ­ Indirect Proof.notebook

16

November 19, 2013

Quizzie Poo