Dividing a Triangle by Connecting the Midpoints of its Sides

Question

If $T$ is any triangle. Suppose we connect the midpoints of its sides forming four triangles. Does these four triangles have the same angles?

Answer 1

Hint:

If $ABC$ are the vertex of the triangle and $M,N$ are the midpoint of $AB$ and $AC$ note that :

$$ \dfrac{AM}{AB}=\dfrac{AN}{AC}=\dfrac{1}{2} \quad and \quad \angle MAN =\angle BAC $$ and use the criterion of similarity (3) here to show that $ABC$ is similar to $AMN$.

You can do the same for the other triangles.