Similar Triangles

Front

What are similar triangles?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is the AA criterion for triangle 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 SSS criterion for triangle similarity?

Back

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

Front

What is the SAS criterion for triangle similarity?

Back

If two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

How do you set up a proportion for similar triangles?

Back

By comparing the lengths of corresponding sides of the triangles.

Front

If triangle ABC is similar to triangle DEF, and AB = 6, AC = 9, and DE = 12, what is the length of DF?

Back

DF = 8 (using the proportion AB/DE = AC/DF).

Front

What is the relationship between the areas of 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 two similar triangles are in the ratio 2:3, what is the ratio of their areas?

Back

The ratio of their areas is 4:9 (since (2^2):(3^2) = 4:9).

Front

How can you find the length of a side in a similar triangle?

Back

By using the proportion of the corresponding sides and cross-multiplying to solve for the unknown length.

Front

What is a scale factor in similar triangles?

Back

The ratio of the lengths of corresponding sides of two similar triangles.