Similar Figures

Front

What are similar figures?

Back

Similar figures are shapes 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 does it mean for two figures to be proportional?

Back

Two figures are proportional if the ratios of their corresponding side lengths are equal.

Front

If two triangles are similar, what can we say about their angles?

Back

If two triangles are similar, their corresponding angles are equal.

Front

What are corresponding sides?

Back

Corresponding sides are sides in the same position in two similar figures.

Front

How do you find the height of an object using shadows?

Back

You can find the height of an object using similar triangles formed by the object and its shadow, comparing it to another object with a known height and shadow length.

Front

If a tree's shadow is 32 feet long and a 5-foot tall alien's shadow is 8 feet long, what is the height of the tree?

Back

The height of the tree is 20 feet.

Front

What is the scale factor in similar figures?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar figures.

Front

If parallelogram PQRS is similar to parallelogram WXYZ, and the length of side PQ is 6 units, what is the length of side WX if the scale factor is 2?

Back

The length of side WX is 12 units.

Front

What is the relationship between the areas of two similar figures?

Back

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

Front

If the scale factor between two similar triangles is 3:1, what is the ratio of their areas?

Back

The ratio of their areas is 9:1.