Proving Similar Triangles

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, then the triangles are similar.

Front

What is the SSS similarity theorem?

Back

SSS stands for 'Side-Side-Side Similarity', which states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the SAS similarity theorem?

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, then the triangles are similar.

Front

Can you use SSS or SAS without checking the ratios of the sides?

Back

No, you must check the ratios of the sides to confirm similarity using SSS or SAS.

Front

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

Back

The triangles are similar by the AA similarity theorem.

Front

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

Back

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

Front

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

Back

In similar triangles, corresponding angles are equal.

Front

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

Back

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

Front

What is the Side Splitter Theorem?

Back

The Side Splitter Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Front

How can you prove that two triangles are not similar?

Back

If the corresponding angles are not equal or the ratios of the corresponding sides are not equal, the triangles are not similar.