Question

the steps shown can be used to prove that the medians of a triangle meet at a point. which is the final step to complete the proof? write a linear equation for each side of the triangle. write an expression for the midpoint of ac and bc. show that af is congruent to bd and ce. show that af is the median of bc. 1. define segments bd and ce as medians of triangle abc. 2. write linear equations for bd and ce.

Explanation:

To prove that the medians of a triangle meet at a point (the centroid), we first define the medians. Then we write linear - equations for them. After finding the intersection point of two medians, we need to show that the third median also passes through that point. One way to do this in the context of congruence is to show that the segments related to the medians are congruent in a way that implies they all meet at the same point. Among the given options, showing that $\overline{AF}$ is congruent to $\overline{BD}$ and $\overline{CE}$ helps in the overall proof of the concurrency of medians.

Answer:

Show that $\overline{AF}$ is congruent to $\overline{BD}$ and $\overline{CE}$.