Question

Name all the points shown that must be midpoints of the sides of the large triangle.

Short answer

D and E are midpoints of the large triangle.

Step-by-step solution

Step 1. Consider the diagram.

Consider the large triangle ABC.

Step 2. State the explanation.

Here, line DE is parallel to line FC. Also, line DE is parallel to line BC.

$AD=DB=9$ (Given)

D is the midpoint of BA.

Hence, according to the midpoint theorem, line DE is parallel to line BC and D is the midpoint of BA then E must be the midpoint of like AC. Also, DF is not parallel to EC. So, F is not the midpoint of line BC.

Thus, D and E are midpoints of the large triangle.

Step 3. State the conclusion.

Therefore, D and E are midpoints of the large triangle.