Triangle Similarity Theorems

Front

What does AA stand for in triangle similarity?

Back

AA stands for Angle-Angle similarity criterion, which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Front

What does SAS stand for in triangle similarity?

Back

SAS stands for Side-Angle-Side similarity criterion, which states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar.

Front

What does SSS stand for in triangle similarity?

Back

SSS stands for Side-Side-Side similarity criterion, which states that if the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

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

Back

The corresponding angles of similar triangles are congruent.

Front

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

Back

The corresponding sides of similar triangles are proportional.

Front

What is the relationship between the areas of two similar triangles?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Front

How can you prove that two triangles are similar using the AA criterion?

Back

To prove that two triangles are similar using the AA criterion, you need to show that two angles of one triangle are congruent to two angles of the other triangle.

Front

What is the significance of the included angle in the SAS similarity criterion?

Back

The included angle in the SAS similarity criterion must be congruent for the triangles to be considered similar.

Front

Can two triangles be similar if only one pair of angles is congruent?

Back

No, two triangles cannot be similar if only one pair of angles is congruent; at least two pairs of angles must be congruent.

Front

What is the formula for finding the ratio of the sides of similar triangles?

Back

The ratio of the sides of similar triangles is equal to the ratio of any two corresponding sides.