2B Similar Polygons Flashcard

Front

What are similar polygons?

Back

Similar polygons are polygons 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 the symbol \( \sim \) represent in geometry?

Back

The symbol \( \sim \) indicates that two figures are similar.

Front

If two polygons are similar, how do you find the ratio of their corresponding sides?

Back

The ratio of the lengths of corresponding sides of similar polygons is constant and is called the scale factor.

Front

What is the scale factor if the lengths of corresponding sides are 4 cm and 8 cm?

Back

The scale factor is \( \frac{4}{8} = \frac{1}{2} \).

Front

How do you solve for a variable in similar polygons?

Back

Set up a proportion using the lengths of corresponding sides and solve for the variable.

Front

Given \( MNPQ \sim RSTU \), if \( MN = 4 \) and \( RS = 8 \), what is the scale factor?

Back

The scale factor is \( \frac{MN}{RS} = \frac{4}{8} = \frac{1}{2} \).

Front

If \( MNPQ \sim RSTU \) and \( PQ = 6 \), what is the length of \( ST \) if the scale factor is \( \frac{1}{2} \)?

Back

\( ST = PQ \times 2 = 6 \times 2 = 12 \).

Front

What is the relationship between the areas of two similar polygons?

Back

The ratio of their areas is the square of the ratio of their corresponding side lengths.

Front

If the scale factor of two similar polygons is \( \frac{1}{3} \), what is the ratio of their areas?

Back

The ratio of their areas is \( \left(\frac{1}{3}\right)^2 = \frac{1}{9} \).

Front

How do you find the missing angle in similar polygons?

Back

The missing angle can be found since corresponding angles in similar polygons are equal.