#### Answer

The proof is in the following form:
Column 1 of proof; Column 2 of proof.
Thus, we have:
1. The midpoint of both sides breaks the sides into even segments; definition of a midpoint.
2. The two sides of the original triangle are proportional to the two sides of the new triangle; this follows from (1).
3. The angle shared is congruent to itself; identity property
4. The two triangles are similar; SAS

#### Work Step by Step

By theorem the segment joining two midpoint of two sides of a triangle is parallel to the base.
Therefore, the corresponding angles are congruent $ \angle M = \angle N $
the two triangles AMN and ABC are similar by AA.
$\square$