Dynamic Activity

Similarity in Right Triangles

Lesson Vocabulary

• geometric mean

Take note Theorem 7-3

Theorem

The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.

If …

△ A B C white up pointing triangle eh b c  is a right triangle with right ∠ A C B , angle eh c b comma  and C D ¯ c d bar  is the altitude to the hypotenuse

Then …

△ A B C ∼ △ A C D white up pointing triangle eh b c , tilde operator white up pointing triangle eh c d

△ A B C ∼ △ C B D white up pointing triangle eh b c , tilde operator white up pointing triangle c b d

△ A C D ∼ △ C B D white up pointing triangle eh c d , tilde operator white up pointing triangle c b d