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 does AA~ stand for in triangle similarity?

Back

AA~ stands for Angle-Angle Similarity Postulate, which states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What does SSS~ stand for in triangle similarity?

Back

SSS~ stands for Side-Side-Side Similarity Postulate, which states that if the corresponding sides of two triangles are in proportion, the triangles are similar.

Front

What does SAS~ stand for in triangle similarity?

Back

SAS~ stands for Side-Angle-Side Similarity Postulate, which states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, the triangles are similar.

Front

How can you determine if two triangles are not similar?

Back

If none of the similarity postulates (AA~, SSS~, SAS~) apply, the triangles are not similar.

Front

If two triangles have one angle of 60° and another angle of 30°, what can be said about their similarity?

Back

They are similar by AA~ because they have two equal angles.

Front

If triangle ABC has sides of lengths 3, 4, and 5, and triangle DEF has sides of lengths 6, 8, and 10, are they similar?

Back

Yes, they are similar by SSS~ because the sides are in proportion (3:6, 4:8, 5:10).

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle XYZ is similar to triangle PQR, and the length of side XY is 5 cm and side PQ is 10 cm, what is the ratio of their sides?

Back

The ratio of their sides is 1:2.

Front

What is the formula to find the length of a side in similar triangles?

Back

If triangles are similar, the ratio of corresponding sides is equal to the ratio of their corresponding altitudes.