Proportions and Similar Triangles

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

What are similar triangles?

Back

Similar triangles are triangles 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

If triangle ABC is similar to triangle DEF, what can be said about their corresponding sides?

Back

The ratios of the lengths of corresponding sides of triangle ABC and triangle DEF are equal.

Front

How do you determine if two triangles are similar using angle-angle (AA) similarity?

Back

If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the Side-Side-Side (SSS) similarity criterion?

Back

If the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the Side-Angle-Side (SAS) similarity criterion?

Back

If one angle of a triangle is equal to one angle of another triangle and the sides including those angles are in proportion, then the triangles are similar.

Front

Solve for k: 3/5 = k/15

Back

k = 9

Front

If AB/DE = AC/DF, what does this indicate?

Back

This indicates that triangles ABC and DEF are similar by the Side-Side-Side (SSS) similarity criterion.

Front

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

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Front

If the sides of triangle ABC are 4, 6, and 8, and triangle DEF is similar to triangle ABC with a scale factor of 2, what are the lengths of the sides of triangle DEF?

Back

The sides of triangle DEF are 8, 12, and 16.