Proof 4.
Let ABC be any triangle. Let D be a point on AC. Prove that there is a dissection of ABC into a trapezoid PQRS.
What condition is necessary on the point D for this to work?
Proof: Let ABC be any triangle. Let D be a point on . Decompose this triangle into four sections are shown above. Using isometries, we can rearrange these shapes into a trapezoid. In order for the decomposed shapes to form a trapezoid, point D must be equivalent to point I or . When this occurs, each of the sides are equal in length. This allows for a set of parallel lines to exist which satisfies the definition of a trapezoid.