Similarity and Proportions

Front

What is similarity in geometry?

Back

Similarity in geometry refers to two figures that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of corresponding sides are proportional.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

How do you find the missing side length in similar polygons?

Back

To find the missing side length in similar polygons, set up a proportion using the lengths of corresponding sides. Cross-multiply and solve for the unknown.

Front

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

Back

If two triangles are similar, their corresponding angles are equal.

Front

What is the scale factor in similar figures?

Back

The scale factor is the ratio of the lengths of two corresponding sides of similar figures. It indicates how much one figure has been enlarged or reduced compared to the other.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 4 cm and side DE is 8 cm, what is the scale factor?

Back

The scale factor is 2:1, meaning triangle DEF is twice the size of triangle ABC.

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 sides of two similar triangles are in the ratio 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 3²:5², which simplifies to 9:25.

Front

How do you solve for x in a proportion?

Back

To solve for x in a proportion, cross-multiply the terms and then isolate x. For example, if a/b = c/x, then ax = bc.

Front

What is the definition of corresponding sides in similar figures?

Back

Corresponding sides in similar figures are the sides that are in the same relative position in each figure.