2020 DL Similarity Theorems

Front

What is the definition of 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

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

Back

The corresponding angles of similar triangles are equal.

Front

If triangle ABC is similar to triangle DEF, and AB = 4, AC = 6, and DE = 8, what is the length of DF?

Back

DF = 12 (Using the ratio of similarity: AB/DE = AC/DF).

Front

What is the Side-Angle-Side (SAS) similarity theorem?

Back

If an angle of one triangle is equal to an angle of another triangle and the sides including these angles are in proportion, then the triangles are similar.

Front

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

Back

If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

How do you set up a proportion for similar triangles?

Back

You can set up a proportion by comparing the lengths of corresponding sides of the triangles.

Front

If triangle XYZ is similar to triangle PQR, and XY = 5, YZ = 10, and PQ = 15, what is the length of QR?

Back

QR = 30 (Using the ratio of similarity: XY/PQ = YZ/QR).

Front

What is the definition of a proportion in the context of similar triangles?

Back

A proportion is an equation that states that two ratios are equal.

Front

If the lengths of two sides of a triangle are 6 and 9, what is the ratio of these sides?

Back

The ratio is 2:3.

Front

What is the relationship between the sides of similar triangles?

Back

The lengths of corresponding sides of similar triangles are proportional.