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### 12 Cards in this Set

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 Geometric mean If a, b and x are positive numbers with a/x=x/b, then x is the geometric mean between a and b Complete the theorem: If the altitude is drawn to the hypotenuse of a right triangle, then the 2 triangles formed... are similar to the original triangle and to each other. Complete the corollary: When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude... is the geometric mean between the segments of the hypotenuse Complete the corollary: When the altitude is drawn to the hypotenuse of a right triangle, each leg... is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg Pythagorean Theorem In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. Converse of the Pythagorean Theorem If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. Common right triangle lengths (3,4,5), (6,8,10), (9,12,15), (12,16,20), (15,20,25)/(5,12,13), (10,24,26), (15,36,39), (20,48,52), (25,60,65)/(8,15,17), (16,30,34), (24,45,51), (32,60,68), (40,75,85)/ (7,24,25), (14,48,50), (21,72,75), (28,96,100), (35,120,125) Complete the theorem: If c^2=a^2+b^2, then... the measure of angle c=90 & triangle ABC is a right triangle Complete the theorem: if c^2a^2+b^2, then the measure of angle C>90 and Triangle ABC is an obtuse triangle 45º-45º-90º Theorem In a 45º-45º-90º triangle, the hypotenuse is the square root of 2 times as long as the leg 30º-60º-90º Theorem In a 30º-60º-90º triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of 3 times as long as the shorter leg.