Geometry B 9.7 Similar and Congruent Shapes

Front

What are similar shapes?

Back

Shapes that have the same shape but not necessarily the same size. Their corresponding angles are equal, and the lengths of corresponding sides are proportional.

Front

What are congruent shapes?

Back

Shapes that are identical in shape and size. All corresponding sides and angles are equal.

Front

What is a scale factor?

Back

A number that scales, or multiplies, some quantity. In geometry, it is the ratio of the lengths of two corresponding sides of similar shapes.

Front

If two shapes are similar with a scale factor of 3/4, what does this mean?

Back

It means that the lengths of the sides of one shape are 3/4 the lengths of the corresponding sides of the other shape.

Front

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

Back

The ratio of their areas is the square of the scale factor.

Front

If two cones are similar with a scale factor of 3/4, what is the ratio of their surface areas?

Back

The ratio of their surface areas is (3/4)² = 9/16.

Front

What does it mean if two shapes are neither similar nor congruent?

Back

It means that the shapes do not have the same shape or size, and their corresponding angles and sides are not proportional.

Front

How do you determine if two shapes are congruent?

Back

By checking if all corresponding sides and angles are equal.

Front

What is the ratio of the surface areas of two similar pyramids with a scale factor of 1/2?

Back

The ratio of their surface areas is (1/2)² = 1/4.

Front

What is the formula for the surface area of a cone?

Back

Surface Area = πr(r + l), where r is the radius and l is the slant height.