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, the triangles are similar (AA ~).

Front

What is the SSS criterion for triangle similarity?

Back

If the lengths of the corresponding sides of two triangles are in proportion, the triangles are similar (SSS ~).

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, the triangles are similar (SAS ~).

Front

How do you find the scale factor of similar triangles?

Back

The scale factor is found by dividing the lengths of corresponding sides of the two triangles.

Front

If triangle ABC is similar to triangle DEF, and AB = 6, DE = 9, what is the scale factor?

Back

The scale factor is 9/6 or 3/2.

Front

If two triangles are not similar, what can be concluded about their angles and sides?

Back

Their corresponding angles are not equal, and their corresponding sides are not in proportion.

Front

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

Back

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

Front

If triangle XYZ is similar to triangle PQR with a scale factor of 2:3, what is the ratio of their areas?

Back

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

Front

What does it mean if two triangles are said to be 'not similar'?

Back

It means that the triangles do not have the same shape; their angles and sides do not correspond in a proportional manner.