Similar Triangles AA SSS SAS

Determine whether the triangles are similar. Explain your reasoning.

Answer explanation

Corresponding sides are not proportional

While on vacation, Gatlin is standing next to a palm tree at his hotel and wants to use his shadow to help measure the palm tree. Gatlin is 6 feet 3 inches tall, and his shadow is 9 feet 9 inches long. If the length of the tree’s shadow is 38 feet 6 inches, about how tall is the palm tree?

• 6 feet

• 24.7 feet

• 60.1 feet

• There is not enough information given to determine the height of the palm tree.

Answer explanation

Convert the inches to decimals

3 in = .25 ft

6 in = .5 ft

9 in = .75 ft

Then sketch right triangles to help you identify corresponding sides.

The Power Tower ride at Cedar Point amusement park is casting a shadow that is 76 feet long. Addy is 5 ft 6 in tall and her shadow is 18 in long. About how tall is the Power Tower (round to the nearest tenth if necessary).

• 300 ft

• 207.2 ft

• 278.7 ft

• 20.7 ft

Answer explanation

$\frac{x}{76}=\frac{5.5}{1.5}$

• SAS~

• SSS~

• AA~

• Not similar ~

• SSS~

• SAS~

• AA~

• Not Similar

• SSS~

• SAS~

• AA~

• Not similar

• SSS~

• SAS~

• AA~

• Not similar

• SSS~

• SAS~

• AA~

• Not similar

• SSS~

• SAS~

• AA~

• Not similar

• SSS~

• SAS~

• AA~

• Not similar