Problem
GEO-B1-M07-P004 Complete a Parallelogram
#4
★☆☆☆☆ Level 1 of 5
In triangle \(ABC\), draw through \(B\) a line parallel to \(AC\), and through \(C\) a line parallel to \(AB\). Let them meet at \(D\). Prove that \(ABDC\) is a parallelogram.
Check the two pairs of opposite sides.
By construction, \(BD\parallel AC\) and \(CD\parallel AB\). Therefore in quadrilateral \(ABDC\), both pairs of opposite sides are parallel. Hence \(ABDC\) is a parallelogram.
The simplest way to “add the missing vertex”.