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Which of the following is NOT a similarity criterion of traingles?a) AA b) SAS c) AAA d) RHS

Question

Which of the following is NOT a similarity criterion of triangles?

a) AA
b) SAS
c) AAA
d) RHS

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Solution

To determine which of the given options is NOT a similarity criterion of triangles, we need to understand what each criterion represents.

a) AA (Angle-Angle): This criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

b) SAS (Side-Angle-Side): This criterion states that if two sides of one triangle are proportional to two sides of another triangle, and the included angles are congruent, then the triangles are similar.

c) AAA (Angle-Angle-Angle): This criterion states that if all three angles of one triangle are congruent to all three angles of another triangle, then the triangles are similar.

d) RHS (Right Angle-Hypotenuse-Side): This criterion is NOT a similarity criterion of triangles. It is actually a congruence criterion for right triangles. It states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Therefore, the correct answer is d) RHS, as it is not a similarity criterion of triangles.

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