Proving Triangles Similar & Similar Triangles

Front

What does AA~ stand for in triangle similarity?

Back

AA~ stands for Angle-Angle similarity, 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, 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, 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

Two triangles are not similar if none of the AA~, SSS~, or SAS~ conditions are met.

Front

If two triangles have two pairs of equal angles, what can be concluded?

Back

The triangles are similar by the AA~ criterion.

Front

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

Back

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

Front

If triangle C has sides of lengths 5, 12, and 13, and triangle D has sides of lengths 10, 24, and 26, are they similar?

Back

Yes, triangle C and triangle D are similar by SSS~.

Front

What is the relationship between similar triangles and their corresponding angles?

Back

In similar triangles, corresponding angles are equal.

Front

What is the relationship between similar triangles and their corresponding sides?

Back

In similar triangles, the lengths of corresponding sides are in proportion.

Front

If triangle E 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°.