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 their corresponding sides are in proportion.

Front

How do you set up a proportion for similar figures?

Back

To set up a proportion, you compare the ratios of the lengths of corresponding sides of the similar figures. For example, if figure A has sides a1 and a2, and figure B has sides b1 and b2, the proportion is a1/a2 = b1/b2.

Front

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

Back

32 feet

Front

What is the relationship between the angles of similar triangles?

Back

In similar triangles, corresponding angles are congruent (equal in measure).

Front

If two figures are similar, what can be said about their corresponding sides?

Back

The lengths of corresponding sides of similar figures are in proportion.

Front

If a triangle has sides of lengths 3, 4, and 5, what are the lengths of the sides of a similar triangle if the shortest side is 6?

Back

The sides of the similar triangle would be 6, 8, and 10.

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 two similar solids have a scale factor of 2:3, what is the ratio of their volumes?

Back

The ratio of their volumes is 2^3:3^3, which simplifies to 8:27.

Front

How can you find a missing side in similar figures?

Back

You can find a missing side by setting up a proportion using the lengths of the corresponding sides of the similar figures.

Front

If Marvin's son is 3 ft tall and casts a shadow of 1 ft, and Marvin casts a shadow of 2.5 ft, how tall is Marvin?

Back

7.5 ft