Similar Figures Using Proportions

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 triangles to be similar?

Back

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

Front

How do you determine if two figures are similar?

Back

To determine if two figures are similar, check if their corresponding angles are equal and if the ratios of the lengths of their corresponding sides are equal.

Front

What is the proportionality constant in similar figures?

Back

The proportionality constant is the ratio of the lengths of corresponding sides of two similar figures.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 6 and side DE is 9, what is the ratio of similarity?

Back

The ratio of similarity is 6:9 or 2:3.

Front

If two similar triangles have a ratio of 2:5, and the length of one side of the smaller triangle is 8, what is the length of the corresponding side in the larger triangle?

Back

The length of the corresponding side in the larger triangle is 20.

Front

What is the formula for finding the missing side in similar triangles?

Back

If triangle ABC is similar to triangle DEF, then (AB/DE) = (BC/EF) = (AC/DF). Use this proportion to find the missing side.

Front

If two similar figures have a scale factor of 4, what does this mean for their areas?

Back

If the scale factor is 4, the area of the larger figure is 4^2 = 16 times the area of the smaller figure.

Front

What is the relationship between the perimeters of similar figures?

Back

The ratio of the perimeters of similar figures is equal to the ratio of their corresponding side lengths.

Front

If the sides of two similar rectangles are in the ratio 3:7, what is the ratio of their areas?

Back

The ratio of their areas is 3^2:7^2, which is 9:49.