How to prove that the line joinning the midpoints of the diagonals of trapezium is parallel to the parallel sides of the trapezium? > 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

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:

![enter image description here](

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...