Similar Figures and Scale Factors

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

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In the context of similar figures, it is the ratio of the lengths of corresponding sides.

Front

How do you determine if two figures are similar?

Back

Two figures are similar if their corresponding angles are equal and the lengths of their corresponding sides are in proportion.

Front

What does it mean for sides to be in proportion?

Back

Sides are in proportion when the ratios of the lengths of corresponding sides of two figures are equal.

Front

If the scale factor from figure A to figure B is 3, what does this mean?

Back

This means that each side of figure B is 3 times longer than the corresponding side of figure A.

Front

Are all angles in similar figures congruent?

Back

Yes, all corresponding angles in similar figures are congruent (equal).

Front

If triangle DEF is similar to triangle ABC with a scale factor of 2, what is the relationship between their corresponding sides?

Back

The lengths of the sides of triangle DEF are half the lengths of the corresponding sides of triangle ABC.

Front

What is the scale factor if the lengths of corresponding sides are 4 cm and 8 cm?

Back

The scale factor is 2, since 8 cm divided by 4 cm equals 2.

Front

How can you find the length of a side in a similar figure if you know the length in the original figure?

Back

Multiply the length of the side in the original figure by the scale factor to find the length in the similar figure.

Front

If two triangles have a scale factor of 1:3, what can you say about their areas?

Back

The area of the larger triangle is 9 times the area of the smaller triangle, since area scales with the square of the scale factor.