Question

JKLM is a rhombus. JL² + KM² = 4JK².
M is the top left corner, L is in the top right, K is in the bottom right, and J is in the bottom left.

Answer 1

Do you need a proof for the statement
JL² + KM² = 4JK²
?

In geometry, it is always a good idea to start with drawing a figure of the given situation. It is informative and inspiring.


Hints:
If we inscribe the rhombus in a rectangle ABCD as shown above, we see that JL=BC and KM=AB.
Show that JL^2+KM^2=AB^2+BC^2=AC^2.
Finally, show the relation between AC and JK using similar triangles.