Honors Geometry - Right Triangle Altitude Theorem

Front

What is the Right Triangle Altitude Theorem?

Back

The Right Triangle Altitude Theorem states that the altitude drawn to the hypotenuse of a right triangle creates two smaller right triangles that are similar to each other and to the original triangle.

Front

If CD is the altitude to hypotenuse AB in triangle ABC, what is the relationship between the segments AD, DB, and the altitude CD?

Back

The relationship is given by the formula: CD^2 = AD * DB.

Front

In a right triangle, if the hypotenuse is 16 and one segment of the hypotenuse is 4, what is the length of the other segment?

Back

The length of the other segment is 12, since the hypotenuse is divided into two segments AD and DB, where AD + DB = hypotenuse.

Front

How do you find the length of the altitude in a right triangle using the segments of the hypotenuse?

Back

Use the formula: CD = √(AD * DB), where AD and DB are the segments of the hypotenuse.

Front

What is the significance of the altitude in a right triangle?

Back

The altitude helps in determining the area of the triangle and establishes relationships between the sides of the triangle.

Front

If AB = 16 and DB = 4, what is the length of BC using the Right Triangle Altitude Theorem?

Back

BC = 8, calculated using the relationship from the theorem.

Front

What is the formula for the area of a right triangle?

Back

Area = (1/2) * base * height.

Front

In triangle ABC, if AD = 4 and DB = 16, what is the length of the altitude CD?

Back

CD = 8, calculated using the formula CD = √(AD * DB).

Front

What is the relationship between the areas of the smaller triangles formed by the altitude in a right triangle?

Back

The areas of the two smaller triangles are proportional to the lengths of the segments of the hypotenuse.

Front

If the altitude of a right triangle is known, how can you find the lengths of the segments of the hypotenuse?

Back

You can use the relationship: CD^2 = AD * DB to find the segments if one segment is known.