Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What characterizes similar triangles?

1. Equal side lengths

2. Equal angles and proportional sides

3. Right angles only

4. Isosceles properties

The correct answer is: Equal angles and proportional sides

Similar triangles are characterized by having equal angles and proportional sides. This means that while the triangles may differ in size, the corresponding angles match perfectly, and the lengths of their corresponding sides are in a constant ratio. Because the angles are equal, this leads to the proportionate relationship between the sides, making it possible to determine that the triangles share the same shape, regardless of their dimensions. For example, if two triangles have one angle of 30 degrees and another angle of 60 degrees, the third angle would necessarily also be 90 degrees, confirming that the triangles are similar. The sides would then follow a specific proportion, such that if one triangle's sides measure 2, 4, and 6, the other could be 1, 2, and 3, maintaining the same ratio of side lengths. Other given choices do not accurately reflect the defining properties of similar triangles. Equal side lengths pertain to congruent triangles, right angles do not by themselves indicate similarity, and isosceles properties relate specifically to triangles with at least two equal sides, which is not a requirement for similarity. Thus, the key features of similarity hinge solely on the equal angles and the proportional relationship of the sides.