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, then the triangles are similar.

Front

What is the SSS criterion for triangle similarity?

Back

If the sides of one triangle are in proportion to the sides of another triangle, then the triangles are similar.

Front

What is the SAS criterion for triangle similarity?

Back

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

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 sides: AB/DE = AC/DF => 4/8 = 6/DF => DF = 12).

Front

What is a proportion in the context of similar triangles?

Back

A statement that two ratios are equal, often used to compare the lengths of corresponding sides of similar triangles.

Front

If two triangles are similar, how do you find the length of a missing side?

Back

Set up a proportion using the lengths of the corresponding sides and solve for the missing length.

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, and the ratio of XY to PQ is 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 9:25 (since (3/5)² = 9/25).

Front

How can you determine if two triangles are similar using side lengths?

Back

By checking if the ratios of the lengths of corresponding sides are equal.