Final answer:
False. Two exterior angles drawn at any vertex of a triangle are not always congruent.
Step-by-step explanation:
False. At any vertex of a triangle, two remote interior angles can be drawn, not exterior angles. These remote interior angles are always congruent to their corresponding exterior angles, but the exterior angles themselves are not necessarily congruent.
For example, let's consider a triangle with vertices A, B, and C. At vertex A, we can draw two remote interior angles: angle BAC and angle CAB. These two angles are congruent to their corresponding exterior angles, which are angle ABC and angle ACB respectively. However, angle ABC and angle ACB may not be congruent to each other. It depends on the specific triangle.
Therefore, it is not true that two exterior angles drawn at any vertex of a triangle are always congruent.