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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^2<a^2+b^2, then...
the measure of angle c<90 and Triangle ABC is an acute triangle
Complete the theorem: If c^2>a^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.