Similarity of Triangles

Front

What are similar triangles?

Back

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

Front

What is the Angle-Angle (AA) similarity criterion?

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 these angles are in proportion, then the triangles are similar.

Front

How do you write a proportion for similar triangles?

Back

A proportion can be written as a/b = c/d, where a and b are the lengths of corresponding sides of the triangles, and c and d are the lengths of the other corresponding sides.

Front

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

Back

The ratio of their sides is 4:8 or 1:2.

Front

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

Back

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

Front

If triangle XYZ is similar to triangle PQR, and the ratio of XY to PQ is 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 3²:5² or 9:25.

Front

What does it mean if two triangles are not similar?

Back

It means that their corresponding angles are not equal, or their corresponding sides are not in proportion.

Front

How can you determine if two triangles are similar using a scale factor?

Back

If you can find a scale factor that relates the lengths of corresponding sides, the triangles are similar.