Theorems
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Solution: Since we know that 8 + 11 must be greater than <math>S_3</math>, we have <math>8\ + 11 > S_3</math>, | Solution: Since we know that 8 + 11 must be greater than <math>S_3</math>, we have <math>8\ + 11 > S_3</math>, | ||
so <math>S_3</math> must be less than 19. But what is the smallest value that <math>S_3</math> can be? | so <math>S_3</math> must be less than 19. But what is the smallest value that <math>S_3</math> can be? | ||
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Well, we know that <math>S_3\ + 11\ must be > 8 </math>, but 11 is already greater than 8 so that doesn't help us. | Well, we know that <math>S_3\ + 11\ must be > 8 </math>, but 11 is already greater than 8 so that doesn't help us. | ||
- | However we also know that <math>S_3\ + 8\ must be > 11 </math>. Using algebra we subtract 8 from both sides of our equation we get <math>S_3\ + 8 {\color{Red}-8}\ must be > 11 {\color{Red}-8} </math> | + | However we also know that <math>S_3\ + 8\ must be > 11 </math>. |
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+ | Using algebra we subtract 8 from both sides of our equation we get <math>S_3\ + 8 {\color{Red}-8}\ must be > 11 {\color{Red}-8} </math> | ||
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[[Category:Geometry]] | [[Category:Geometry]] |
Revision as of 23:10, 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 equation we get