How to prove that the line joining the midpoints of the diagonals of trapezium is parallel to the parallel sides of the trapezium?
I tried to prove this by drawing BD and joining the midpoints of AD and BC. I am unable to prove that this line and the line joining the midpoints of the diagonals are the same, please help
Best Answer
Perhaps it is not surprising that all the segments (not only those that are actually depicted) going through the midpoint of the red line are halved by the same red point:
Taking any trapezium the two diagonals will be parallel to two of the colored lines above. That is, their midpoints will be equidistant to both of the black parallel lines...