# Geometry Ch 7 & 8 vocab

### 19 terms by jesshorsesluv

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### ratio

quotient of two numbers

### proportions

an equation stating that two or more ratios are equal

### extremes

first and fourth terms

### means

second and third terms

### geometric mean

a over x = x over b
a x
--- = ---
x b x= g.m. between a & b

### means-extremes products therom

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

### arithmetic mean

average between two numbers

### similar

same shape, different size

### reduction

shrink, becoming smaller

### 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

### pythagorean triples

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

### 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

### trigonometric ratios a.k.a. SOHCAHTOA

sin <x = opposite 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

Example: