First things first, Ms. Hunt wasn't in class today and we had an assignment that I presume needed to be finished at home. We both had to take notes on chapter 6-1 and we had an in-book assignment to do. The notes are self-explanatory, but if you forgot the in-book assignment:
Page 206: #1-13.
Ok, getting back to the chapter . . .
Example 1:
Given: AC > AB; AB > BC
Conclusion: AC ? BC
AC > BC because of the Properties of Inequality.
What are the properties of inequality? Well, they're a group of properties of . . . inequality. You can use these for proofs, and you would just say Prop. of Inequality as the reason.
Properties of Inequality:
If a > b and c >/= d, then a + c > b + d.
If a > b and c > 0, then ac > bc and (a/c) > (b/c).
If a > b and c < 0, then ac < bc and (a/c) < (b/c).
If a > b and b > c, then a > c.
If a = b + c and c > 0, then a > b.
Example 2:
Given: AC > BC; CE > CD
Prove: AE > BD
Statements: Reasons:
1. AC > BC; CE > CD 1. Given
2. AC + CE > BC + CD 2. Prop. of Inequality
3. AC + CE = AE; BC + CD = BD 3. Segment Addition Postulate
4. AE > BD 4. Substitution Prop.
Example 3:
Given: Angle 1 is an exterior angle of Triangle DEF.
Prove: m Angle 1 > m Angle D; m Angle 1 > m Angle E.
Statements: Reasons:
1. . . . 1. Given
2. m Angle 1 = m Angle D + m Angle E. 2. The measure if an ext. angle of a triangle = the sum of the measures of the two remote int. angles.
3. m Angle 1 > m Angle D; 3. Prop. of Inequality
m Angle 1 > m Angle E
This specific example proves the following theorem:
Theorem 6-1: Exterior Angle Inequality Theorem
The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.
OKAY, so I couldn't find a video about Inequalities in Geometry because it's too broad of a term and all that showed up were different types of inequalities - not even from geometry. So I specified my search to "Properties of Inequalities Geometry" and that came up with nothing except for a 30-minute video of this one guy teaching his class about inequalities, but half of them weren't related to this lesson. Then I just tried to find ANYTHING having to do with this specific lesson and nothing came up. So, what I decided to do, was to give a link to main points of EACH section in Chapter 6. It's basically a link to notes for the whole chapter. I figured this would be helpful to understand mainly what the chapter is about.
TURN OFF YOUR SOUND BEFORE GOING TO THIS LINK, THERE ARE ADDS IN THE SIDEBAR AND THEY'RE LOUD.
http://www.scribd.com/doc/522464/Geometry-Notes-Chapter-Six-Inequalities-in-Geometry
I REALLY hope this link is aloud past the filter.
So, it's that time of the day . . . who will be the next scribe.....?
Yeah, Matthew, you should have known it was going to be you from the beginning. HAVE FUN!
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