Parallelogram Law
Andrew Ellinor
and
Calvin Lin
contributed
This wiki is incomplete.
The parallelogram law is a formula that relates the sides of a parallelogram to its diagonals. Roughly speaking, the sum of the squares of the sides of the parallelogram equals the sum of the squares of the diagonals.
Contents
Statement of the Parallelogram Law
If \(ABCD\) is a parallelogram, then
\[ AB^2 + BC^2 + CD^2 + DA^2 = AC^2 + BD ^2 .\]
Proof of the Parallelogram Law
Parallelogram Law as a Special Case in Other Quadrilaterals
For a rectangle, ...
Relation to the Dot Product of Vectors
Cite as:
Parallelogram Law.
Brilliant.org.
Retrieved from
https://brilliant.org/wiki/parallelogram-law/