Geometric Mean in Right Triangles

The video tutorial explains the concept of geometric mean in right triangles, focusing on the relationships formed when an altitude is drawn to the hypotenuse. It provides examples to illustrate how each leg of the triangle is the geometric mean between the adjacent part of the hypotenuse and the entire hypotenuse. The tutorial includes calculations for specific examples, emphasizing the importance of exact answers over rounded values.

What is created when the altitude is drawn to the hypotenuse of a right triangle?

• A new triangle

• Geometric mean relationships

• A parallel line

• An isosceles triangle

In the geometric mean rule, each leg of the right triangle is the geometric mean between which two segments?

• The part of the hypotenuse next to the leg and the whole hypotenuse

• The adjacent side and the opposite side

• The altitude and the hypotenuse

• The base and the height

If the part of the hypotenuse next to a leg is 8 and the whole hypotenuse is 14, what is the geometric mean of the leg?

• Square root of 112

• 12

• 10

• Square root of 196

What is the simplified form of the square root of 112?

• 16√2

• 8√2

• 2√28

• 4√7

In the second example, if the leg is 10 and the part of the hypotenuse next to it is 6, what is the whole hypotenuse?

• 16

• 12

• B

• 20

What is the value of B if 6/B = 10/10?

• 16.6

• 20

• 10

• 16 and 2/3

Why is it preferred not to round off the answer to 16.6 in the second example?

• Because it is easier to calculate

• Because it is a rule of geometry

• Because it is more accurate to leave it as a fraction

• Because decimals are not allowed