To verify the mid-point theorem for a triangle.
The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
Two lines are parallel if they do not meet at any point.
Two triangles are congruent if their corresponding angles and corresponding sides are equal.
Two triangles are similar if their corresponding angles equal and their corresponding sides are in proportion.
PQ || BC and PQ=1/2 BC
To prove ▲ APQ ≅ ▲ QRC
Since midpoints are unique, and the lines connecting points are unique, the proposition is proven.