Similar Figures and 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 their corresponding sides are in proportion.

Front

How do you find the missing side of similar figures using proportions?

Back

To find the missing side of similar figures, set up a proportion using the lengths of corresponding sides. For example, if two triangles are similar, you can write the proportion as (side1/side2) = (missing side/known side) and solve for the missing side.

Front

What is the definition of proportion in mathematics?

Back

A proportion is an equation that states that two ratios are equal. It can be expressed as a/b = c/d, where a, b, c, and d are numbers.

Front

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

Back

The corresponding angles of similar triangles are equal.

Front

What is the formula for finding the scale factor between two similar figures?

Back

The scale factor is found by dividing the length of a side of one figure by the length of the corresponding side of the other figure.

Front

How can 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 proportional.

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 scale factor of two similar figures is 3:2, what is the ratio of their areas?

Back

The ratio of their areas would be 3^2:2^2, which simplifies to 9:4.

Front

What is the significance of the term 'corresponding sides' in similar figures?

Back

Corresponding sides are the sides of similar figures that are in the same relative position. They are used to set up proportions when solving for unknown lengths.

Front

How do you solve for an unknown side in a proportion?

Back

To solve for an unknown side in a proportion, cross-multiply the known values and then isolate the variable. For example, if a/b = c/x, then cross-multiply to get ax = bc, and solve for x.