Similar Triangles

Front

What is the definition of similar triangles?

Back

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

Front

What does it mean for sides of similar triangles to be proportional?

Back

It means that the ratios of the lengths of corresponding sides of the triangles are equal.

Front

What are corresponding angles in similar triangles?

Back

Corresponding angles are angles that are in the same relative position in similar triangles. They are equal in measure.

Front

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

Back

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

Front

How can you determine if two triangles are similar?

Back

Two triangles can be determined to be similar if they satisfy one of the following criteria: AA (Angle-Angle), SSS (Side-Side-Side), or SAS (Side-Angle-Side) similarity.

Front

What is the AA criterion for triangle similarity?

Back

The AA criterion states that 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

The SSS criterion states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

What is the SAS criterion for triangle similarity?

Back

The SAS criterion states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 4 cm and side DE is 8 cm, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.

Front

If the lengths of two corresponding sides of similar triangles are 5 cm and 15 cm, what is the scale factor?

Back

The scale factor is 1:3.