ABCD is a quadrilateral with G and H the mid points of line DA and DC respectively. Show that line AB + line DC = 2GH
Given a quadrilateral with and the midpoints of line and respectively.
Consider triangle
A midsegment of a triangle is a line segment which joins the midpoints of two sides of the triangle. It is parallel to the third side and has a length equal to half the length of the third side. Hence
Consider the square with side
Consider right triangle By the Pythagorean Theorem
Hence
The statement line AB + line DC = 2GH for a quadrilateral is False in our case.
In the example below
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