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 their corresponding sides are proportional.

Front

What is the criteria 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 proportional.

Front

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

Back

The corresponding angles of similar figures are equal.

Front

If the sides of two similar triangles are in the ratio 2:3, what does this imply about their areas?

Back

The areas of the two triangles are in the ratio of the squares of the sides' ratio, which is 4:9.

Front

How do you find a missing side in similar figures?

Back

To find a missing side in similar figures, set up a proportion using the lengths of the corresponding sides.

Front

What is a similarity statement?

Back

A similarity statement indicates that two figures are similar, using the symbol '∼'. For example, ΔABC ∼ ΔDEF.

Front

What does it mean if two figures are not similar?

Back

If two figures are not similar, it means that their corresponding angles are not equal or the ratios of their corresponding sides are not proportional.

Front

In a pair of similar triangles, if one triangle has sides of lengths 4, 6, and 8, what could be the lengths of the corresponding sides of the other triangle if the ratio is 1:2?

Back

The corresponding sides of the other triangle would be 8, 12, and 16.

Front

What is the relationship between the lengths of sides and 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 a rectangular garden is 45 ft wide and 70 ft long, and the width on a blueprint is 9 in, how do you find the length on the blueprint?

Back

Set up a proportion: 45 ft / 70 ft = 9 in / x in, where x is the length on the blueprint. Solve for x to find it is 14 in.