ch 8.1-8.3 geometry

quiz review

geometric mean

• when the means of a proportion are the same number

• between two numbers, the positive square root of their product

geometric mean (altitude) theorem

the altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. the length of this altitude is the geometric mean between the lengths of these two segments

geometric mean (leg) theorem

know what proportions this creates (draw it out)

pythagorean theorem

• right triangle

• a²+b²=c²

pythagorean triple

• 3,4,5

• 5,12,13

• 8,15,17

• 7,24,25

(and what you would get if you multiplied them each by x)

acute triangles

c²<a²+b²

obtuse

c²>a²+b²

triangle inequality theorem

the sum of the lengths of any two sides of a triangle must be greater than the length of the third side

45-45-90 triangle

• leg #1 & leg #2 = 1

• hypotenuse = square root of 2

30-60-90 triangle

• leg #1 = 1

• leg #2 = square root of 3

• hypotenuse = 2