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 proportional.

Front

What is the AA (Angle-Angle) Similarity Postulate?

Back

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Front

What is the SSS (Side-Side-Side) Similarity Theorem?

Back

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

Front

What is the SAS (Side-Angle-Side) Similarity Theorem?

Back

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

How do you write a similarity statement?

Back

A similarity statement shows that two triangles are similar, using the symbol '~'. For example, ΔABC ~ ΔDEF.

Front

What does it mean if corresponding angles are not congruent?

Back

It means that the triangles cannot be similar, as one of the conditions for similarity is that corresponding angles must be equal.

Front

What does it mean if corresponding sides are not proportional?

Back

It indicates that the triangles cannot be similar, as one of the conditions for similarity is that corresponding sides must be in proportion.

Front

Provide an example of a similarity statement using SSS similarity.

Back

If ΔIJK and ΔHFG have sides in proportion, you can write: ΔIJK ~ ΔHFG by SSS similarity.

Front

Provide an example of a similarity statement using AA similarity.

Back

If ΔTUV and ΔTSR have two angles congruent, you can write: ΔTUV ~ ΔTSR by AA similarity.

Front

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

Back

It indicates that triangles XYZ and NEW are similar, meaning their corresponding angles are equal and their corresponding sides are proportional.