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 in similar figures to be proportional?

Back

In similar figures, the lengths of corresponding sides are in the same ratio, meaning that if one side of a triangle is twice as long as the corresponding side of another triangle, all other corresponding sides will also be twice as long.

Front

What is the significance of congruent angles in similar triangles?

Back

In similar triangles, all corresponding angles are congruent, which means they have the same measure. This is a key property that helps establish the similarity of triangles.

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) criterion, SSS (Side-Side-Side) similarity criterion, or SAS (Side-Angle-Side) similarity criterion.

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 two 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, what can be said about their corresponding sides?

Back

If triangle ABC is similar to triangle DEF, then the ratios of the lengths of their corresponding sides are equal.

Front

If the sides of two similar triangles are in the ratio 2:3, what can be said about their areas?

Back

The areas of two similar triangles are in the ratio of the squares of the lengths of their corresponding sides. Therefore, if the sides are in the ratio 2:3, the areas are in the ratio 2²:3² or 4:9.

Front

What is a similarity statement?

Back

A similarity statement is a mathematical statement that indicates that two figures are similar. For example, ΔLMN ∼ ΔPQO indicates that triangle LMN is similar to triangle PQO.