Theorems
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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 <math>S_3</math>) | 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 <math>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> | + | 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 | + | so <math>S_3</math> must be less than 19. But what is the smallest value that <math>S_3</math> can be? |
+ | 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 -8 must be > 11 -8 </math> | ||
[[Category:Geometry]] | [[Category:Geometry]] |
Revision as of 23:04, 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