Geometric Mean

1
Geometric Mean the Pythagorean Thm.

• Section 7-1 7-2

2

• The geometric mean between 2 positive numbers a
  and b is the positive number x where
• x2 ab
• x

3
Thm. 7-1

• If the altitude is drawn from the vertex of
  the right angle of a right triangle to its
  hypotenuse, then the 2 triangles formed are
  similar to the given triangle and to each other.

4
C
B
A
D
5
Thm. 7-2

• The measure of the altitude drawn from the
  vertex of the right angle of a right triangle to
  its hypotenuse is the geometric mean between the
  measures of the 2 segments of the hypotenuse.

6
h
a
b
7
Thm. 7-3

• If the altitude is drawn to the hypotenuse of
  a right triangle, then the measure of a leg of
  the triangle is the geometric mean between the
  measures of the hypotenuse and the segment of the
  hypotenuse adjacent to that leg.

8
a
b
h
d
e
c
9
Pythagorean Theorem

• In a right triangle, the sum of the squares of
  the measures of the legs equals the square of the
  measure of the hypotenuse.

c
a
a2 b2 c2
b
Converse is also true.
10
Pythagorean Triples

• If the measures of a right triangle are whole
  numbers, the measures of the sides are a
  Pythagorean triple.
• 3-4-5 5-12-13 8-15-17
• 7-24-25

11
Joke Time

• What is a twip?
• A twip is what a wabbit takes when he wides on a
  twain.

12

• What is gray, has big ears and has a trunk?
• A mouse going on vacation