Problem
GEO-B1-M07-P018 Move a Segment by a Parallelogram
#18
★★★☆☆ Level 3 of 5
In triangle \(ABC\), complete parallelogram \(ABDC\). Prove that segment \(AB\) can be replaced by equal segment \(CD\), and segment \(AC\) by equal segment \(BD\).
Use the properties of opposite sides of a parallelogram.
Opposite sides of a parallelogram are equal. Therefore in \(ABDC\), \(AB=CD\) and \(AC=BD\). This is why a completed parallelogram often lets us move a segment to a convenient place.
A toolbox problem: the goal is to understand the function of the construction.