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 a large triangle ABC.

Step 2. State the explanation.

Here,

$AD=DB=x$ (Given)

$AE=EC=y$ (Given)

$BF=z$

$FC=z+1$

Therefore, $BF\ne FC$

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.