Right Triangles and Trigonometry

1
Right Trianglesand Trigonometry

• Chapter 9

2
Chapter 9

• 9.1 Similar Right Triangles
• 9.2 Pythagorean Theorem
• 9.3 Converse of the Pythagorean Theorem
• 9.4 Special Right Triangles
• 9.5 Trigonometric Ratios
• 9.6 Solving Right Triangles
• 9.7 Vectors

3
Similar Right Triangles

• 9.1

4
Theorem 9.1

• If the altitude is drawn to the hypotenuse of a
  right triangle, then the two triangles formed are
  similar to the original triangle and to each
  other.

5
Theorem 9.2

• In a right triangle, the altitude from the right
  angle to the hypotenuse divides the hypotenuse
  into two segments.
• The length of the altitude is the geometric mean
  of the lengths of the two segments.

6
Theorem 9.2
7
Theorem 9.3

• In a right triangle, the altitude from the right
  angle to the hypotenuse divides the hypotenuse
  into two segments.
• The length of each leg of the right triangle is
  the geometric mean of the lengths of the
  hypotenuse and the segment of the hypotenuse that
  is adjacent to the leg.

8
Theorem 9.3
9
Theorem 9.3
10
Find the measure of x.

• A
• B
• C
• D

11
Find the measure of y.

• A
• B
• C
• D