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Level 111

Pythagorean Theorem


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The Converse of the Pythagorean Theorem
If the lengths of the 3 sides of a triangle satisfy the Pythagorean Equation (a²+b₂=c₂), then the triangle is a right triangle.
Isosceles Right Triangle Conjecture
In an isosceles right triangle, if the legs have length l, then the hypotenuse has length l√2.
30°-60°-90° Triangle Conjecture
In a 30°-60°-90° triangle, if the shorter leg has length a, then the longer leg has length a√3 & the hypotenuse has length 2a.
Distance Formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
exponent
A mathematical notation indicating the number of times a quantity is multiplied by itself
Squared
A number with an exponent of 2 is often said to be
Right Triangle
A triangle with one right angle.
Pythagorean Theorem
in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs
Leg
The shortest sides of a right triangle. Usually called a and b
Hypotenuse
in a right triangle, the side opposite the right angle
Square Root
when multiplying a number by itself to get a square number
Radical
(noun) a sign placed in front of an expression to denote that a root is to be extracted.
radical form
the form in which you leave an answer when the square root is not known and a calculator is not provided.
Pythagorean Triples
A set of positive integers a,b, and c such that it fits into the pythagorean formula.