Today we learned about 2 very special right triangles: the 45-45-90 and 30-60-90 triangles. They have side lengths with special relationships.
Theorem: In a 45-45-90 degree triangle, the length of the hypotenuse is the square root of 2 times the length of the legs. (note: the legs are congruent; it's an isosceles right triangle)
Theorem: In a 30-60-90 degree triangle, the length of the hypotenuse is twice the length of the shorter leg, while the longer leg is the square root of 3 times the length of the shorter leg.
These theorems look a lot better on a diagram...
We worked out a few examples in class. The nice thing about these triangles is that you don't need the Pythagorean theorem to find missing sides. Also, you only need to know the length of one side to find the other two.
This lesson is one of the most important in geometry. You will use these special right triangles over and over again in trigonometry... unfortunately, you will not see this applied until your junior year. Hold on to your learning!
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