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Geometry - Ch. 8
Chapter 8 Vocabulary, Postulates, and Theorems
38
Mathematics
9th Grade
04/16/2013

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Term
8.1
geometric mean
Definition
the geometric mean of two numbers is the positive square root of their product
Term
KeyConcept
Definition
The geometric mean of two positive numbers a and b is the number x such that:

a/x = x/b . So, x² = ab
Term
Theorem
Definition
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.
Term
Theorem
Definition
The altitude drawn to the hypotenuse of a right triangle seperates the hypotenuse into two segments, The length of this altitude is the geometric mean between the lengths of those two segments.
Term
Theorem
Definition
The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. the length of a leg of this triangle is the geometric mean between the l[ength of the hypotenuse and the segment of the hypotenuse adjacent to that leg.
Term
8.2
theorem
Definition
In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
Term
pythagorean triple
Definition
set of three non-zero whole numbers a, b, and c, such that a²+b²=c².
Term
Key Concept
Definition
Common Pythagorean Triples:

3,4,5
3x,4x,5x
5,12,13
5x,12x,13x
8,15,17
8x,15x,17x
7,24,25
7x,24x,25x
Term
Theorem
Definition
If the sum of the squares of the lengths of the shortest sides of a triangle is equal to the square of the length of the shortest side, then the triangle is a right triangle.
Term
Theorem
Definition
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 other two sides, then the triangle is an acute triangle.
Term
Theorem
Definition
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 the two other sides, then the triangle is an obtuse triangle.
Term
ordered triple
Definition
the location of a point in space
Term
8.3
Theorem
Definition
In a 45-45-90 triangle, the legs l are congruent and the length of the hypotenuse h is √2 times the length of a leg.
Term
Theorem
Definition
In a 30-60-90 triangle, the lenth of the hypotenuse h is 2 times the length of the shorter leg ssled and the lenth of the longer leg lleg is √3 times the length of sleg.
Term
8.4
trigonometry
Definition
study of the measures of triangles
Term
trigonometric ratio
Definition
ratio of the lengths of two sides of a right triangle.
Term
sine
Definition
sine = opposite over hypotenuse
Term
cosine
Definition
cosine = adjacent over hypotenuse
Term
tangent
Definition
tangent= opposite over adjacent
Term
inverse sine
Definition
the angle whose sine is x.
Term
inverse cosine
Definition
the angle whose cosine is x.
Term
inverse tangent
Definition
the angle whose tangent is x.
Term
8.5
angle of elevation
Definition
angle formed by a horizonal line and an observer's line of sight to an object above the horizontal line
Term
angle of depression
Definition
angle formed by a horizontal line and an observer's line of sight to an object that is below the horizontal line.
Term
8.6
law of sines
Definition
used to find lengths and angle measures for any triangle
Term
Theorem
Definition
law of sine

sinA sinB sinC
---- = ---- = ----
a b c
Term
Theorem
Definition
Law of Cosines:

a²= b² + c² - 2bc(cosA)
b²= a² + c² - 2ac(cosB)
c²= a² + b² - 2ab(cosC)
Term
Law of Cosine
Definition
Used to find triangles if you know the measures of two sides and an included angle.
Term
ambiguous case
Definition
the case in which triangles are determined?
Term
8.7
vector
Definition
describes both magnitude and direction of a quantity
Term
magnitude
Definition
length of vector from initial point to its terminal point
Term
direction
Definition
the angle that it forms with the horizontal line or as a meaurement between 0 and 90 on a north-south east-west line
Term
resultant
Definition
sum of two or more vectors
Term
parallelogram method
Definition
one method to add vectors
Term
triangle method
Definition
another method to add vectors
Term
standard position
Definition
if the initial point of the vector is at the origin.
Term
component form
Definition
to describe a vector with any initial point, use this, which describes the vector in terms of its horizontal component x an vertical component y
Term
Key Concept
Definition
If a,b and c,d are vectors and k is a scalar, then the following are true.
a,b + c,d = a+c,b+d
a,b - c,d = a-c, b-d
k(a,b) = ka, kb
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