Question

Which of the following sets of triangles are similar according to the Angle-Angle Similarity Postulate?

equilateral triangles

equiangular triangles

both equilateral and equiangular triangles

neither equilateral nor equiangular triangles

Answer: both equilateral and equiangular triangles

Answer 1

Both equilateral and equiangular triangles are similar by the Angle-Angle Similarity Postulate because they each have two congruent angles with any other triangle of the same type.

Step-by-step explanation:

The Angle-Angle (AA) Similarity Postulate states that two triangles are similar if two angles of one triangle are congruent to two angles of the other triangle. Equilateral triangles are similar by AA postulate because all angles in any equilateral triangle measure 60 degrees, thus any two will be congruent with any two angles in another equilateral triangle. Equiangular triangles are also similar by the AA postulate, as all their corresponding angles are equal. Consequently, both equilateral and equiangular triangles are similar according to the AA Similarity Postulate.

Answer 2

Yes

Both equilateral and equiangular triangles

Step-by-step explanation:

The AA (Angle-Angle) similarity states that if two pairs of corresponding angles are congruent, then the triangles are similar

In equilateral triangles, all angles are equal.The corresponding sides of two equilateral triangles are congruent thus they will be similar. An Equiangular triangle is also an equilateral triangle because its interior angles are the same and add up to 180°.