Altitudes of Right Triangles and Geometric Mean

Front

What is the altitude of a right triangle?

Back

The altitude of a right triangle is the perpendicular segment from a vertex to the line containing the opposite side.

Front

How do you find the area of a right triangle using the altitude?

Back

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

Front

What is the geometric mean of two numbers a and b?

Back

The geometric mean is the square root of the product of the two numbers: √(a*b).

Front

In a right triangle, how does the altitude relate to the two segments it creates on the hypotenuse?

Back

The altitude creates two segments on the hypotenuse that are proportional to the lengths of the other two sides of the triangle.

Front

If the lengths of the legs of a right triangle are 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: hypotenuse = √(3² + 4²) = 5.

Front

What is the relationship between the altitude and the hypotenuse in a right triangle?

Back

The altitude to the hypotenuse is the geometric mean of the two segments it creates on the hypotenuse.

Front

How do you calculate the length of the altitude from the hypotenuse in a right triangle?

Back

Altitude = (leg1 * leg2) / hypotenuse.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

If the altitude of a right triangle is 4 and the base is 6, what is the area?

Back

Area = 1/2 * 6 * 4 = 12.

Front

What is the significance of the geometric mean in right triangles?

Back

It helps in finding the lengths of segments created by the altitude on the hypotenuse.