FYI, using an Approach0 search, there's the AoPS thread Mid-line of a trapezoid. There is also the closely related Trapezium Midsegment Theorem, where its answer states that what you are asking about is the Trapezoid Midsegment Theorem.
Given trapezoid ABCD with bases AB and CD, draw diagonals AC and BD. Let E be the midpoint of AC and F the midpoint of BD. Prove that E and F lie on the midsegment of ...
A line segment between the midpoints of 2 edges of a triangle is called a midsegment. What I would like to know: Is there a general use word for a line segment connecting the midpoints of 2 sides of any shape? (In particular, I'd like to know the answer to the question in the title.
I need a hint on how to prove that "In a triangle ABC if D is the midpoint of the side AB and the line through D intersects AC at E such that BC=2DE then E is the midpoint of AC and BC is para...
I thought about this question when I thought why median and altitude of an equilateral triangle are the same. And it seems to me it is all because the vertex is directly above the midpoint. Though...
