# M4 Geometery (Ch. 8 and 9)

## 27 terms

### ratio

quotient of two numbers

rise over run

### proportions

an equation stating that two or more ratios are equal

### extremes

first and fourth terms

### means

second and third terms

### means-extremes products therom

product of the means = product of the extremes (cross multipling)

### means-extremes ratio therom

if product of pair of nonzero numbers = product of another pair of nonzero numbers, one of either pairs are extremes and the other are means

means are equal

### arithmetic mean

average between two numbers

### similar

same shape, different size

enlargment

### reduction

shrink, becoming smaller

### similar polygons

1. ratios of corresponding sides are equal
2. corresponding angles are congruent
3. ratio of perimeter = ratio of any corresponding sides

### proving similar trianges

AA (angle-angle)
SSS (corresponding sides are proportional)
SAS (two corresponding sides are proportional and included angle is congruent)

### side-splitter therom

if a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides proportionally

### angle bisector therom

if a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides

a²+b²=c²

### distance formula

d = √[( x₂ - x₁) + (y₂ - y₁)], d = √[( x₂ - x₁)² + (y₂ - y₁)²]

### pythagorean triples

any three whole numbers that satisfy the equation a²+b²=c²
ex: (3,4,5) (6,8,10) (9,12,15)

### 30-60-90 triangle

opposite of 30 = x
opposite of 60 = x√3
opposite of 90 (hypotenuse) = 2x

### 45-45-90 triangle

opposite of 45's = x
opposite of 90 = x√2

### slant height

The height of a triangular face of a pyramid

### altitude

the perpendicular distance from the base of a geometric figure to opposite vertex (or side if parallel)

### cube

rectangular solid with all congruent faces

### trigonometric ratios

sin <x = opposite leg/hypotenuse
cos <x = adjacent leg/hypotenuse
tang <x = opposite leg/adjacent leg

### angle of elevation

the angle formed by a horizontal line and the line of sight to an object above the horizontal line

### angle of depression

the angle formed by a horizontal line and the line of sight to an object below the horizontal line