Theorems
From MHSHS Wiki
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==External Angle Theorem== | ==External Angle Theorem== | ||
===Thm: An external angle is equal to the sum of the two opposite interior angles.=== | ===Thm: An external angle is equal to the sum of the two opposite interior angles.=== | ||
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+ | ==Vertical Angle Theorem== | ||
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+ | ==Supplementary Angle Theorem== | ||
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+ | ==Complementary Angle Theorem== | ||
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+ | ==The Sum of the Interior Angles of a Triangle== | ||
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+ | ==External Angle Theorem== | ||
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+ | ==SAS - SSS Triangle Congruence Theorems== | ||
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+ | ==The Sum of the Interior Angles of any Polygon== | ||
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+ | ==The Measure of Each Interior Angle of a Regular Polygon== | ||
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+ | ==The Measure of Each Exterior Angle of a Regular Polygon== | ||
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+ | ==The Sum of the Exterior Angles of any Polygon== | ||
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[[Category:Geometry]] | [[Category:Geometry]] |
Revision as of 23:48, 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).