Proving Similar Triangles

Front

What does AA similarity mean in triangles?

Back

AA similarity (Angle-Angle) means that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What does SAS similarity mean in triangles?

Back

SAS similarity (Side-Angle-Side) means that 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

What does SSS similarity mean in triangles?

Back

SSS similarity (Side-Side-Side) means that if the three sides of one triangle are in proportion to the three sides of another triangle, then the triangles are similar.

Front

How can you determine if two triangles are similar?

Back

You can determine if two triangles are similar by using the AA, SAS, or SSS similarity postulates.

Front

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

Back

The triangles are similar by the AA similarity postulate.

Front

If two triangles have one pair of equal angles and the sides including those angles are in proportion, what can be concluded?

Back

The triangles are similar by the SAS similarity postulate.

Front

If the sides of two triangles are in proportion, what can be concluded?

Back

The triangles are similar by the SSS similarity postulate.

Front

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

Back

The included angle is the angle between the two sides being compared; it must be equal for the triangles to be similar.

Front

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

Back

No, if two triangles have no equal angles, they cannot be similar.

Front

What is an example of AA similarity?

Back

If triangle ABC has angles of 30°, 60°, and 90°, and triangle DEF has angles of 30°, 60°, and 90°, then they are similar by AA similarity.