Similar triangles

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 the lengths of their corresponding sides are proportional.

Front

What is the AA criterion for triangle similarity?

Back

The AA (Angle-Angle) criterion 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 criterion for triangle similarity?

Back

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

Front

What is the SAS criterion for triangle similarity?

Back

The SAS (Side-Angle-Side) criterion 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

How can you determine if two triangles are similar using angle measures?

Back

If the sum of the angles in both triangles is equal to 180 degrees and at least two angles are equal, the triangles are similar.

Front

What does it mean if two triangles are not similar?

Back

If two triangles are not similar, it means that their corresponding angles are not equal, and/or their corresponding sides are not in proportion.

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

How do you complete a proportion involving similar triangles?

Back

To complete a proportion, you can cross-multiply and solve for the unknown side length.

Front

What is the significance of the sum of angles in a triangle?

Back

The sum of the angles in any triangle is always 180 degrees, which is a fundamental property used to determine triangle similarity.

Front

What is the relationship between corresponding sides of similar triangles?

Back

The lengths of corresponding sides of similar triangles are proportional, meaning the ratio of one side to the corresponding side in another triangle is constant.