Integral values of a, b, and c, where a, b, and c Pythagorean Triples: are relatively prime: 3 - 4 - 5 (the most common) 5 - 12 - 13 8 - 15 - 17 20 - 21 - 7 - 24 - 25 29 12 - 35 - 9 - 40 - 41 37 The 45o - 45o - 90o right triangle, or triangle: This is right isosceles half of a square, where the legs are congruent. If the leg is then s, the is (s times the square root of 2). Example: A hypotenuse s * sqrt(2) square has a perimeter of 10, and you need to know the length of the diagonal. s = 2.5, so d = 2.5 * sqrt(2). The 30o - 60o - 90o right triangle: This is half of an triangle. The short leg, the one opposite the 30o angle, equilateral is the hypotenuse is and the long leg, which is opposite the s, 2s, 60o angle, is (s times the square root of 3). s * sqrt(3) I've seen so many different Number of diagonals in an polygon: s-sided applications of this formula: s (s - 3) / 2 where s is the number of sides of the polygon. A polygon having 45 sides has 45*(45-3)/2 = 945 diagonals. You must know these backward, Fraction, decimal, percent equivalencies: forward, and upside down. The halves, thirds, fourths, fifths, sixths, sevenths, (yes, sevenths!), (so hard, eighths, ninths,tenths, he?), It also helps to know elevenths, twentieths, twenty-fifths, fiftieths. the and You should, for example, be able to twelfths, fifteenths, sixteenths. recognize, instantly and without hesitation, that 83 1/3% is 5/6, and that 9/11 is 81 9/11%. Space diagonal of a cube: s * sqrt(3)
Pythagorean Triples: Integral values of a, b, and c, where a, b, and c are relatively prime: 3 - 4 - 5 (the most common) 5 - 12 - 13 8 - 15 - 17 7 - 24 - 25 20 - 21 - 29 9 - 40 - 41 12 - 35 - 37 The 45o - 45o - 90o right triangle, or right isosceles triangle: This is half of a square, where the legs are congruent. If the leg is s, then the hypotenuse is s * sqrt(2) (s times the square root of 2). Example: A square has a perimeter of 10, and you need to know the length of the diagonal. s = 2.5, so d = 2.5 * sqrt(2). The 30o - 60o - 90o right triangle: This is half of an equilateral triangle. The short leg, the one opposite the 30o angle, is s, the hypotenuse is 2s, and the long leg, which is opposite the 60o angle, is s * sqrt(3) (s times the square root of 3). Number of diagonals in an s-sided polygon: I've seen so many different applications of this formula: s (s - 3) / 2 where s is the number of sides of the polygon. A polygon having 45 sides has 45*(45-3)/2 = 945 diagonals. Fraction, decimal, percent equivalencies: You must know these backward, forward, and upside down. The halves, thirds, fourths, fifths, sixths, sevenths, (yes, sevenths!), eighths, ninths,tenths, (so hard, he?), elevenths, twentieths, twenty-fifths, fiftieths. It also helps to know the twelfths, fifteenths, and sixteenths. You should, for example, be able to recognize, instantly and without hesitation, that 83 1/3% is 5/6, and that 9/11 is 81 9/11%. Space diagonal of a cube: s * sqrt(3)