Question

prove by vectors that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

Answer 1

Let the sides be a,b,c,d where a=c and b=d because its a parallelogram. 
Let the diagonals be e and f. 
Let the angles of the parallelogram be X and Y (2 of each) 
By the law of cosines: 
e^2 = a^2 + b^2 - 2ab*cosX 
f^2 = a^2 + b^2 - 2ab*cosY 
e^2 + f^2 = 2(a^2+b^2) - 2ab(cosX + cosY) 

but 2X + 2Y = 360 in a parallelogram. 
X+Y = 180 
X = 180 - Y 
cosX = -cosY 
cosX + cosY = 0 
so: 
e^2 + f^2 = 2(a^2+b^2) = a^2+b^2+c^2+d^2

Answer 2

Answer:

Step-by-step explanation:

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