Theorems
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However we also know that <math>S_3\ + 8\ must\ be > 11 </math>. | However we also know that <math>S_3\ + 8\ must\ be > 11 </math>. | ||
- | Using algebra we subtract 8 from both sides of our inequality we get <math>S_3\ + 8 {\color{Red}-8}\ > 11 {\color{Red}-8} </math>, so <math>S_3\ > 3</math>. Our final answer is <math>3 < S_3\ < 19</math>. | + | Using algebra we subtract 8 from both sides of our inequality we get <math>S_3\ + 8 {\color{Red}-8}\ > 11 {\color{Red}-8} </math>, so <math>S_3\ > 3</math>. Our final answer is <math>3 < S_3\ < 19</math> (our third side must be greater than 3 but less than 19). |
[[Category:Geometry]] | [[Category:Geometry]] |
Revision as of 23:19, 18 October 2009
The Distance Formula
Example: Find the distance between point A(5,-7) and B(-6,-2) and leave your answer in radical form.
Solution: Let A be point 1 and B be point 2. We have
Substituting we have
Try some distance problems at Distance & Midpoint 9-2 ME Worksheet
Sum of the Sides of a Triangle
Thm: The sum of two sides of any triangle must be greater than the third side
Example: Given two sides of a triangle are 8 inches and 11 inches, find all the possible lengths of the third side (also known as S3)
Solution: Since we know that 8 + 11 must be greater than S3, we have , so S3 must be less than 19. But what is the smallest value that S3 can be?
Well, we know that , but 11 is already greater than 8 so that doesn't help us.
However we also know that .
Using algebra we subtract 8 from both sides of our inequality we get , so . Our final answer is (our third side must be greater than 3 but less than 19).