In parallelogram EFGH, let M be the midpoint of side EF, and let N be the midpoint of side EH. Line segments FH and GM intersect at P, and line segments FH and GN intersect at Q. Find PQ/FH. You don't need to give an answer if you don't have one. A hint or a diagram would be just as helpful. Thanks!
+118608 In parallelogram EFGH, let M be the midpoint of side EF, and let N be the midpoint of side EH. Line segments FH and GM intersect at P, and line segments FH and GN intersect at Q. Find PQ/FH. You don't need to give an answer if you don't have one. A hint or a diagram would be just as helpful. Thanks!
Here is a link to an adjustable graph. I do not remember sharing a link to a GeoGebra graph before so I will be interested in whether it works. I suppose it will....
https://www.geogebra.org/classic/wbfqyt8g
I haven't worked an answer yet.
+118608 I still have not worked out how to do the general case, however, a square is a special case of a parallelogram.
The question implies that the answer will always be the same.
so...
If you look at this specific case (A square of side length 2)
distance HF is easy to work out
then work out the coordinates of Q
then distance OQ can be found.
Now you can finish it.
Yes! Good to realize in this situation we can assume it is a square and then know it is true.
+118608 We can't really.
We certainly have not proven that this is a general ratio.
However, the question did not ask us to prove anything and it implied that the answer would always be the same.
So it follows that if we find it for a specific case then we will have the answer that is being asked for.
