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, which states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What is the SSS~ similarity criterion?

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~ mean in the context of 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 similar using AA~?

Back

If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar by AA~.

Front

What is the significance of the similarity statement ΔXYZ~ΔNEW?

Back

It indicates that triangle XYZ is similar to triangle NEW, meaning their corresponding angles are equal and their corresponding sides are in proportion.

Front

Can two triangles be similar if they have no equal angles?

Back

No, two triangles cannot be similar if they have no equal angles, as similarity requires at least two pairs of equal angles.

Front

What is an example of using the SSS~ criterion?

Back

If triangle ABC has sides of lengths 3, 4, and 5, and triangle DEF has sides of lengths 6, 8, and 10, then 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 two triangles are similar, what can be said about their areas?

Back

The areas of similar triangles are in the ratio of the squares of the lengths of their corresponding sides.