Question

If ARSU -- AVST, then the triangles are similar by:

a) The SSS similarity theorem.
b) The AA similarity postulate.
c) The SAS similarity theorem.

Answer 1

Triangles ARSU and AVST are similar by the Angle-Angle (AA) similarity postulate since they have two pairs of corresponding angles that are congruent.

Step-by-step explanation:

If ARSU is congruent to AVST, the triangles are similar by the Angle-Angle (AA) similarity postulate. This postulate states that two triangles are similar if they have two pairs of corresponding angles that are congruent. In the given situation, we have two pairs of angles that match: ∠A is common in both triangles, ∠R in the first triangle is congruent to ∠V in the second, and ∠S is congruent to ∠T. Thus, with two angles being the same, we confirm that the triangles are similar by AA, which means the corresponding sides are in the same ratio.