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 12, what is the area of the triangle?

Back

Area = 1/2 * 20 * 12 = 120.

Front

What is the Pythagorean theorem?

Back

In a right triangle, a² + b² = c², where c is the hypotenuse and a, b are the other two sides.

Front

How can you find the length of the altitude if you know the lengths of the two segments it creates?

Back

Use the formula: altitude = sqrt(segment1 * segment2).

Front

What is the significance of the altitude in triangle similarity?

Back

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

Front

If the segments created by the altitude are 9 and 16, what is the length of the altitude?

Back

Altitude = sqrt(9 * 16) = sqrt(144) = 12.

Front

What is the formula for the area of a triangle using the hypotenuse and altitude?

Back

Area = 1/2 * hypotenuse * altitude.

Front

How does the altitude affect the angles of the triangle?

Back

The altitude creates right angles with the hypotenuse, affecting the triangle's angle measures.