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.
$\square$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/c7561ae3-c8da-4e8e-904d-7ca53899c82c/steps_image/small_1589813339.jpeg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T013427Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=8233ca2667fa598e2dca0e3a82dee6a73eb4bb1db5d7d3a5e41dbe7c81599b5f)