Similar Triangle Proofs

Front

What is the definition of similar triangles?

Back

Similar triangles are 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 similarity criterion state?

Back

The AA (Angle-Angle) similarity criterion states 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 criterion state?

Back

The SAS (Side-Angle-Side) similarity criterion states that 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.

Front

What does SSS similarity criterion state?

Back

The SSS (Side-Side-Side) similarity criterion states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is a proportion in the context of similar triangles?

Back

A proportion is an equation that states that two ratios are equal. In similar triangles, the ratios of the lengths of corresponding sides are equal.

Front

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

Back

The corresponding angles of triangle ABC and triangle DEF are equal.

Front

If CB / DM = AC / ?, what is the missing side if the answer is AD?

Back

The missing side is AD, indicating that the sides CB and DM are proportional to AC and AD.

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 determine if two triangles are similar using the AA criterion?

Back

To determine if two triangles are similar using the AA criterion, check if two angles of one triangle are equal to two angles of the other triangle.

Front

What is the significance of the AA similarity criterion in proofs?

Back

The AA similarity criterion is significant because it provides a straightforward way to prove triangle similarity without needing to measure sides.