Answer to Question #202356 in Physics for Festus

Question

ABCD is a quadrilateral with G and H the mid points of line DA and DC respectively. Show that line AB + line DC = 2GH

Answer 1

Consider a triangle ACD. GH is the midline because G and H are midpoints of AD and CD. Thus, AC=2GH.

According to the famous theorem, the sum of two sides of triangle are always greater than the third side. Consider triangle ABC. As we see, AC, being the common base for triangles ABC and ACD, is equal to 2GH. And since in triangle ABC AB+BC>AC by the mentioned theorem, and in triangle ACD AD+CD>AC, all we can show is

$$AB+DC>2GH.$$