Problem
GEO-B1-M07-P013 Median and Equal Sides
#13
★★★☆☆ Level 3 of 5
In triangle \(ABC\), point \(M\) is the midpoint of \(BC\). Extend \(AM\) beyond \(M\) to point \(D\), where \(MD=AM\). Prove that if \(AB=AC\), then \(BD=CD\).
After the construction, parallelogram \(ABDC\) appears.
As in the basic construction, \(ABDC\) is a parallelogram. Therefore \(BD=AC\) and \(CD=AB\). By condition \(AB=AC\), hence \(BD=CD\).
Shows how a constructed parallelogram transfers equality of sides.