Prove theorems about triangles. The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. The Pythagorean Theorem can be proven using triangle similarity.

Sample Practice Questions (3)

In the diagram below,

\overline{A B} ∥ \overline{D E}

. Which statement correctly identifies a pair of similar triangles and the reason for their similarity?

△ A B C \sim △ E D C

by AA similarity

△ A B C \sim △ C D E

by SAS similarity

△ A B C \sim △ D E C

by SSS similarity

△ A B C \sim △ E D C

by ASA similarity

△ P QR

∠ Q = 9 0^{\circ}

. An altitude

QS

is drawn to the hypotenuse

P R

. If

P S = 4

and

S R = 9

, what is the length of

P Q

6

213

25

213

In the diagram of right triangle

A B C

, altitude

\overline{B D}

is drawn to hypotenuse

\overline{A C}

. Which proportion is always true?

\frac{A D}{,} A B = \frac{A B}{,} A C

\frac{A D}{,} B D = \frac{B D}{,} A C

\frac{B D}{,} B C = \frac{B C}{,} A D

\frac{A B}{,} B C = \frac{B D}{,} A C

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