chp 8, units 1 to like, 4? idk

Question 1

If a, b, and x are positive numbers and a/x = x/b, then x is called the-

Answer 1

-geometric mean between a and b

Question 2

EX: Find the geometric mean between 5 and 12

Answer 2

5/x = x/12
√60 = √x^2
x= 2√15

Question 3

EX: Find the geometric mean between 16 and 24

Answer 3

16/x = x/24
√x^2 = √384
x=8√6

Question 4

If the altitude is drawn to the hypotenuse of a right triangle,

Answer 4

then the two triangles formed are similar to the original triangle AND to each other.

Question 5

When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is -

Answer 5

• the geometric mean between the segments of the hypotenuse

Question 6

When the altitude is drawn to the hypotenuse of a right triangle, each leg is the -

Answer 6

• geometric mean between the hypotenuse and segment of the hypotenuse that is adjacent to that leg.

Question 7

Pythagorean Theorem

Answer 7

In a right triangle the square of the hypotenuse is equal to the sum of the squares of the legs

Question 8

The Converse of the Pythagorean Theorem

Answer 8

If the square of one side of a triangle is equal to the sum of the squares of the other two sides then the triangle is a right triangle

Question 9

C^2=a^2 + b^2

Answer 9

The triangle is a right triangle

Question 10

c^2 < a^2 + b^2

Answer 10

The triangle is acute

Question 11

c^2 > a^2 + b^2

Answer 11

The triangle is obtuse

Question 12

What triangle is this?

20, 21, 29

Answer 12

right

Question 13

What triangle is this?

5,12,14

Answer 13

obtuse

Question 14

What triangle is this?

6, 7, 8

Answer 14

acute

Question 15

What triangle is this?

1, 3, √10

Answer 15

right

Question 16

30 - 60 - 90 Theorem

Answer 16

In a 30 - 60 - 90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the shorter leg