Mr. Garlin Similar Triangles Theorems

Front

What is the SAS (Side-Angle-Side) Theorem for similar triangles?

Back

The SAS Theorem 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 AA (Angle-Angle) Criterion state?

Back

The AA 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 (Side-Side-Side) Theorem for similar triangles?

Back

The SSS Theorem states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

How can you determine if two triangles are similar using the AA Criterion?

Back

To determine similarity using the AA Criterion, check if two angles of one triangle are equal to two angles of another triangle.

Front

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

Back

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

Front

Can triangles be similar if only one angle is known?

Back

No, at least two angles must be known to establish similarity using the AA Criterion.

Front

What is a proportional relationship in the context of similar triangles?

Back

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

Front

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

Back

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

Front

If two triangles have sides in the ratio 2:3, are they similar?

Back

Not necessarily; the angles must also be checked for equality to confirm similarity.

Front

What is the relationship between the areas of two similar triangles?

Back

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