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, 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 proportional to the three sides of another triangle, 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 proportional to two sides of another triangle and the included angle is equal, the triangles are similar.

Front

How can you determine if 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

How can you determine if triangles are similar using SSS?

Back

If the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar by SSS.

Front

How can you determine if triangles are similar using SAS?

Back

If two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar by SAS.

Front

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

Back

The included angle is the angle formed between the two sides being compared; it must be equal for SAS similarity to hold.

Front

Can triangles be similar if none of the angles are equal?

Back

No, triangles cannot be similar if none of the angles are equal; at least two angles must be equal for similarity.

Front

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

Back

In similar triangles, the lengths of corresponding sides are proportional.

Front

If triangle ABC is similar to triangle DEF, what can be said about their angles?

Back

If triangle ABC is similar to triangle DEF, then angle A = angle D, angle B = angle E, and angle C = angle F.