Altitude to Hypotenuse

Front

What is the altitude to the hypotenuse in a right triangle?

Back

The altitude to the hypotenuse is a perpendicular segment from the right angle vertex to the hypotenuse, creating two smaller right triangles.

Front

How do you calculate the area of a triangle using the altitude to the hypotenuse?

Back

Area = 1/2 * base * height, where the base is the hypotenuse and the height is the altitude.

Front

What is the relationship between the altitude to the hypotenuse and the segments it creates?

Back

The altitude divides the hypotenuse into two segments, and the relationship can be expressed as: (altitude)^2 = (segment1) * (segment2).

Front

If the hypotenuse is 20 and the altitude is 8, what is the area of the triangle?

Back

Area = 1/2 * 20 * 8 = 80 square units.

Front

What is the formula for finding the length of the altitude to the hypotenuse?

Back

Altitude = (leg1 * leg2) / hypotenuse.

Front

In a right triangle, if one leg is 6 and the other leg is 8, what is the length of the hypotenuse?

Back

Hypotenuse = √(6^2 + 8^2) = √(36 + 64) = √100 = 10.

Front

What is the significance of the altitude in triangle similarity?

Back

The altitude to the hypotenuse creates two smaller triangles that are similar to the original triangle and to each other.

Front

If the segments of the hypotenuse are 12 and 16, what is the length of the altitude?

Back

Altitude = √(12 * 16) = √192 = 8√3.

Front

What is the geometric mean in relation to the altitude to the hypotenuse?

Back

The altitude is the geometric mean of the two segments of the hypotenuse: altitude = √(segment1 * segment2).

Front

How does the altitude affect the properties of a right triangle?

Back

The altitude provides a way to calculate area and establishes relationships between the triangle's sides.