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 ratios of the lengths of their corresponding sides are proportional.

Front

How do you determine if two figures are similar?

Back

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

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. It can be used to solve for unknown values in similar figures.

Front

If a rectangle has a width of 4 cm and a length of 6 cm, what is the ratio of width to length?

Back

The ratio of width to length is 4:6, which simplifies to 2:3.

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. It indicates how much one figure has been enlarged or reduced compared to the other.

Front

If a triangle has sides of 3 cm, 4 cm, and 5 cm, and is similar to another triangle with a side of 6 cm, what are the lengths of the other two sides?

Back

The other two sides are 8 cm and 10 cm, using the scale factor of 2.

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 side lengths of two similar rectangles are in the ratio 1:4, what is the ratio of their areas?

Back

The ratio of their areas is 1:16, since (1:4)² = 1:16.

Front

How can shadows be used to determine heights of objects?

Back

By using the concept of similar triangles, the ratio of the height of an object to the length of its shadow can be set equal to the ratio of the height of another object to its shadow length.

Front

If a garden is 45 ft wide and 70 ft long, and the width on a blueprint is 9 in, what is the length on the blueprint?

Back

The length on the blueprint is 14 in.