Chapter 8 Flashcards
Theorem 8.1
if the altitude is drawn to the hypotenuse of a rt. Δ, then the 2 triangles formed are similar to each other and the original
Geometric Mean Altitude Theorem (Maze)
The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into 2 segments. The length of this altitude is the geometric mean between the lengths of these 2 segments
Geometric Mean (Leg) Theorem
The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into 2 segments. The length of a leg of this triangle is the geometric mean between the length of the hypotenuse and the segment of the hypotenuse adjacent to that leg
Pythagorean Theorem
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
Pythagorean Triple
a set of non-zero whole numbers a, b, and c that satisfy the equation a^2 + b^2 = c^2
Converse of Pythagorean Theorem
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 longest side of the triangle, the triangle is a right triangle
Converse of Inequality Theorem
If the square of the length of the longest side of a triangle is greater than the sum of the squares of the length of the other 2 sides, the triangle is obtuse
a^2+b^2
Pythagorean Inequality Theorem
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, the triangle is acute
a^2 + b^2 > c^2 , triangle is acute
45-45-90 Triangles Theorem
In a 45-45-90 Triangle, both legs are congruent and the length of the hypotenuse is the square root of 2 times the length of a leg
30-60-90 Triangles Theorem
In a 30-60-90 triangle, the length of the hypotenuse is twice that of the short side, and the long side is radical 3 times the length of the short side
Geometric mean
if 2 positive numbers A and B is to the number X such that a/x=x/b so x^2=ab and x is the square root of ab
Trigonometric Ratio
A ratio of the lengths of 2 sides of a right triangle
Sine of an angle
Opposite/Hypotenuse
Cosine of an angle
Adjacent/Hypotenuse
Tangent of an angle
Opposite/adjacent
Inverse sine
sin^-1
Inverse Cosine
Cos^-1
Inverse Tangent
tan^-1
