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# Math 9.1 - 9.7

### Math vocab for chapter 9 (9.1 - 9.7)

Theorem 9.1 If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other
Theorem 9.2 In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments.
Theorem 9.3 In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The lengths of each leg of the right triangle is geometric mean of lengths of hypotenuse and segment of hypotenuse that is adjacent to leg
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. c2=a2+b2
Pythagorean Triple A set of three positive whole numbers a, b, and c that satisfy the equation c2=a2+b2
Converse of the Pythagorean Triple If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides then the triangle is a right triangle.
Theorem 9.6 If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the owth two sides then the triangle is acute
Theorem 9.7 If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of our other two sides then the triangle is obtuse.
Theorem 9.8 In a 45-45-90 triangle the hypotenuse is radical 2 times as long as each leg
Theorem 9.9 In a 30-60-90 triangle the hypotenuse is twice as longas the shorter leg and the longer leg is radical 3 times as long as the shorter leg.
Trigonometric Ratios A ratio of the lengths of two sides of a right triangle. The three basic trigonometric ratios are sine, cosine, and tangent. SOH CAH TOA
Angle of Elevation When you stand and look up at a point in the distance, the angle that your line of makes a line of sight makes with a line drawn horizantally.
Magnitude of a Vector The distance from the initial point to the terminal point of a vector. The magnitude of vector AB is the distance from A to B and is written as Ivector ABI
Direction of a Vector Determined bu the angle that the vector makes with a horizontal line
Equal Vectors Two vectors that have the same magnitude and direction
Prallel Vectors Two vectors that have the same of opposite directions
Adding Vectors: The Sum of Two Vectors The sum of vector u = <a1,b1> and vector v = <a2,b2> is vector u + vector v = <a1+a2, b1+b2>
Created by: jumpthemoon