Triangle Similarity

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the relationship between two triangles that have the same shape but may differ in size. This means their corresponding angles are equal and their corresponding sides are proportional.

Front

What does the AA criterion for triangle similarity state?

Back

The AA (Angle-Angle) criterion states that if two angles of one triangle are equal to two angles of another triangle, then the two 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 proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What does the SSS criterion for triangle similarity state?

Back

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

Front

If triangle A has sides of lengths 3, 4, and 5, and triangle B has sides of lengths 6, 8, and 10, are the triangles similar?

Back

Yes, triangle A and triangle B are similar because the sides are proportional (3:6, 4:8, 5:10).

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

How can you determine if two triangles are similar using the SSS criterion?

Back

To determine if two triangles are similar using the SSS criterion, check if the ratios of the lengths of corresponding sides are equal.

Front

What is a proportional relationship in the context of triangle similarity?

Back

A proportional relationship means that the ratios of the lengths of corresponding sides of two triangles are equal.

Front

If two triangles are similar, what can be said about their areas?

Back

The areas of two similar triangles are proportional to the square of the lengths of their corresponding sides.

Front

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

Back

The included angle in the SAS criterion is the angle formed between the two sides being compared; it must be equal for the triangles to be similar.