Geometric Means in Right Triangles

This video tutorial covers the concept of geometric mean, explaining how to calculate it and apply it in various mathematical contexts, such as right triangles and similar triangles. The tutorial includes step-by-step examples and practice problems to reinforce understanding. It also introduces a theorem related to similar triangles and demonstrates how to use geometric mean to find specific measurements within triangles.

What is the geometric mean of 5 and 45?

• 15

• 10

• 25

• 20

How do you simplify the square root of 180?

• 15√2

• 12√3

• 9√2

• 6√5

What happens when you draw an altitude from the right angle to the hypotenuse in a right triangle?

• It creates three congruent triangles.

• It creates three similar triangles.

• It creates two congruent triangles.

• It creates two similar triangles.

Which of the following is true about the geometric mean in right triangles?

• It is always equal to the hypotenuse.

• It can be used to find the length of the altitude.

• It is always equal to one of the legs.

• It is not applicable in right triangles.

If the hypotenuse of a right triangle is divided into segments of 10 and 5, what is the length of the altitude?

• √50

• 10

• 7.5

• 5

What is the geometric mean of 10 and 15?

• 12

• 12.5

• √150

• 13

In a right triangle, if one leg is 8 and the hypotenuse is 33, what is the length of the other leg using geometric mean?

• 17

• 16

• 15

• 18

How do you find the length of a leg in a right triangle using geometric mean?

• By taking the mean of the hypotenuse and the segment adjacent to the leg.

• By taking the mean of the hypotenuse and the altitude.

• By taking the mean of the hypotenuse and one leg.

• By taking the mean of the two legs.

What is the final height of a statue if the altitude is 19.3 and the base is 5?

• 84.498

• 79.498

• 74.498

• 24.3

Why is understanding geometric means important for SATs?

• It is a common topic in SAT math sections.

• It is only tested in SAT subject tests.

• It is not relevant to SATs.

• It is only useful for advanced math courses.