Question

ABCD is a trapezoid AD parallel to Bc. QT is the line joining the midpoints of non parallel sides. AC cuts QT in W. Show that W is the midpoint of AC.

Answer 1

In trapezoid ABCD, where AD is parallel to BC, and QT connects the midpoints of non-parallel sides AB and CD, point W is the intersection of AC and QT. To show that W is the midpoint of AC, the Midpoint Theorem is applied. This theorem establishes that if a line segment connects the midpoints of two sides of a triangle, then that line segment is parallel to the third side and has a length equal to half of the third side. By demonstrating the similarity of triangles ACQ and TQW and considering the parallelism of QT and AD, it is proven that W is indeed the midpoint of AC.