8-4 Special Right Triangles One of the most important topics covered in geometry

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Presentation transcript:

8-4 Special Right Triangles One of the most important topics covered in geometry -45-45-90 -30-60-90

45°-45°-90° Theorem: in a 45-45-90 triangle, the hypotenuse is times as long as a leg. In basic terms, this means that both legs of a 45-45-90 triangle are congruent, because it is isosceles. And the hypotenuse is whatever a leg is multiplied by

45-45-90 Template My word of advice… This is one of the most important things you will take from geometry, MEMORIZE THIS TEMPLATE AND KNOW HOW TO USE IT

Practice Every time that you use a special right triangle, it is helpful to draw the template next to the triangle you are working with. It is helpful if they are in the same orientation too. Find the missing side lengths 4

2.5

If you are given the side of a 45-45-90 triangle you simply find the hypotenuse by multiplying by If given the hypotenuse, to find the legs, you simply divide the hypotenuse by

Find both missing side lengths

Find the missing side lengths

30°-60°-90° Theorem: In a 30-60-90 right triangle, the hypotenuse is twice as long as the shortest leg, and the longest legs is times as long as the shortest leg Which angle is the smallest? 30, 60, or 90? So what side is the smallest? That is enough information to reconstruct the 30-60-90 template.

12 Given the side opposite the 30° angle. -Double it to find the hypotenuse -Multiply it by to find the other leg. 12

22 Given the side opposite the 90° angle. -Divide it by 2 to find the side opposite the 30° angle (shortest side). -Multiply the shortest side by to find the other leg. 22

Case 1 Given the side opposite the 60° angle. Case 1: Given with a -then use the constant in front to use as your side opposite your 30° angle. -multiply the shortest side by 2 then to get the hypotenuse.

5 Case 2 Given the side opposite the 60° angle. Case 2: Given the length without a -then you divide that side by to find what your shortest side is. -multiply the shortest side by 2 then to get the hypotenuse. 5