G-6.4 FLASHCARD Similar Triangles & Indirect Measurements

Front

What are similar triangles?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

What is the principle of indirect measurement?

Back

A method used to find the height or length of an object by using the properties of similar triangles.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

Their corresponding angles are equal.

Front

If a 6-foot person casts a 2-foot shadow, what is the ratio of height to shadow length?

Back

The ratio is 6:2 or simplified to 3:1.

Front

How do you set up a proportion to find the height of an object using shadows?

Back

Set up the proportion as (height of object)/(length of shadow) = (height of reference)/(length of reference shadow).

Front

What is the height of a flagpole that casts a 10-foot shadow when a 6-foot person casts a 2-foot shadow?

Back

30 feet.

Front

A tree is 72 feet tall and casts a shadow of 12 feet. If another tree casts a shadow of 5 feet, how tall is the second tree?

Back

30 feet.

Front

What is the formula for finding the height of an object using similar triangles?

Back

Height = (Height of reference object) * (Length of shadow of object) / (Length of shadow of reference object).

Front

If a tree is 12 feet tall and casts a shadow of 9 feet, how tall is a building that casts a shadow of 24 feet?

Back

32 feet.

Front

What does it mean for two triangles to be proportional?

Back

It means that the ratios of the lengths of their corresponding sides are equal.