In a trapezium ABCD, if AB||CD, then AC2 BC2 is equal to?

Edit: the new version of the question is false: the left hand side should be AC²+BD². In a trapezium ABCD, if AB||CD, then prove that AC²+BC²=BC²+AD²+2AB*CD? read more

In a trapezium, opposite sides are parallel and equal. hence, AB = CD. therefore. AC^2 -BC^2 = AB^2. AB^2 +BC^2 = AC^2. hence ABC forms a right angled triangle since it follows pythagoras theorem. Hence Angle ABC = 90 deg. A trapezium with any one angle 90 is a rectangle. Hence if AC^2 -BC^2 = AB*CD then we can say that trapezium ABCD is a rectangle. read more

This has nothing to do with AB’s height/length, nor CD’s age. read more