"The sum of the squares of the diagonals is equal

Merati4tmjn

Merati4tmjn

Answered question

2022-05-15

"The sum of the squares of the diagonals is equal to the sum of the squares of the four sides of a parallelogram."
I find this property very useful while solving different problems on Quadrilaterals & Polygon,so I am very inquisitive about a intuitive proof of this property.

Answer & Explanation

Blaine Andrews

Blaine Andrews

Beginner2022-05-16Added 20 answers

Let two sides of the parallelogram correspond to the vectors a and b . Then the diagonals correspond to the vectors a + b and a b , and
( a + b ) 2 + ( a b ) 2 = 2 a 2 + 2 b 2 ,
which is the desired identity between the sums of the squares of the diagonals and the sides.
Tristan Meyers

Tristan Meyers

Beginner2022-05-17Added 5 answers

...and just in case it isn't obvious, in this answer x 2 is used as an abbreviation for x x (inner product).

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