SOLUTION: 890.Trapezoid ABCD has parallel sides AB and CD, of lengths a and b respectively. Diagonals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let

Algebra ->  Geometry-proofs -> SOLUTION: 890.Trapezoid ABCD has parallel sides AB and CD, of lengths a and b respectively. Diagonals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let      Log On


   

Question 1163139: 890.Trapezoid ABCD has parallel sides AB and CD, of lengths a and b respectively. Diagonals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let P and Q be its intersections with AD and BC respectively.
(a) Prove that E is the midpoint of PQ.
(b)Show that PQ=1/(0.5)(1/a + 1/b).
Found 2 solutions by AnlytcPhil, Edwin McCravy:
Answer by AnlytcPhil(1807) About Me  (Show Source):
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
This is a complicated proof. It is found here:

https://www.studyrankersonline.com/18739/point-intersection-diagonals-trapezium-through-segment-drawn-parallel-meeting-prove-that

In the UK the word for "trapezoid" is "trapezium".  The proof there has the
same letters as yours except it has O for your E.

Edwin