SAT Math Multiple Choice Question 963: Answer and Explanation
15. While working on a geometry problem, Raul determines that the angles of one triangleare congruent to the corresponding angles of another triangle. Which of the followingis a valid deduction that Raul can make?
- A. The two triangles are congruent but not necessarily similar.
- B. The two triangles are similar but not necessarily congruent.
- C. The two triangles are both similar and congruent.
- D. The two triangles are neither similar nor congruent.
Correct Answer: B
Category: Additional Topics in Math / Geometry
Strategic Advice: Before you sift through the choices, take some time to consider the differences between similarity and congruence.
Getting to the Answer: One of the easiest ways to understand the difference between similarity and congruence is to think about equilateral triangles. Every equilateral triangle has three angles that all measure 60 degrees, so all equilateral triangles are similar. But of course, equilateral triangles come in all different sizes: They can be tiny or huge and anything in between. Thus, equilateral triangles are usually not congruent. Raul has two triangles whose corresponding angles are all congruent, so the triangles are similar. They are not, however, necessarily congruent, so the answer is (B).