Chapter 8 Flashcards Preview

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Flashcards in Chapter 8 Deck (18):
1

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

2

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

3

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

4

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

5

Pythagorean Triple

a set of non-zero whole numbers a, b, and c that satisfy the equation a^2 + b^2 = c^2

6

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

7

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

8

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

9

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

10

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

11

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

12

Trigonometric Ratio

A ratio of the lengths of 2 sides of a right triangle

13

Sine of an angle

Opposite/Hypotenuse

14

Cosine of an angle

Adjacent/Hypotenuse

15

Tangent of an angle

Opposite/adjacent

16

Inverse sine

sin^-1

17

Inverse Cosine

Cos^-1

18

Inverse Tangent

tan^-1