Similar 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 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 lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the SAS criterion for triangle similarity?

Back

If two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

How can you determine if two triangles are not similar?

Back

If none of the similarity criteria (AA, SSS, SAS) are satisfied, the triangles are not similar.

Front

If triangle ABC is similar to triangle DEF, what can be said about their corresponding angles?

Back

The corresponding angles of triangle ABC and triangle DEF are equal.

Front

If the sides of triangle ABC are 3, 4, and 5, and the sides of triangle DEF are 6, 8, and 10, are the triangles similar?

Back

Yes, because the sides are in proportion (3:6, 4:8, 5:10).

Front

If triangle ABC has angles of 30°, 60°, and 90°, what are the angles of a similar triangle?

Back

The angles of a similar triangle will also be 30°, 60°, and 90°.

Front

What is the relationship between the ratios of the sides of similar triangles?

Back

The ratios of the lengths of corresponding sides 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, because the sides are in proportion (4:8 = 6:DF).