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Chapter 3: Q25P (page 106)

The sum of the squares of the diagonals of a parallelogram is equal to twice the sum of the squares of two adjacent sides of the parallelogram.

Short Answer

Expert verified

The sum of the square of diagonals is equal to two times the sum of the squares of sides of parallelogram.

Step by step solution

01

Concept and formula used

  • If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
  • The sum of the diagonals of the square the sum of all the internal angles of a square is equal to. Both the diagonals are congruent
02

To prove sum of the square of diagonals is equal to two times the sum of the squares of sides of parallelogram.

Consider the following parallelogram,

Write the first diagonal in vector notation as follows,

d1=A+B

Write the second diagonal in vector notation as follows,

d2=B-A

The sum of squares of diagonals is calculated as follows,

d12+d22=(A+B)2+(B-A)2=A2+B2+2AB+B2+A2-2AB=2A2+B2

Therefore, the sum of the squares of diagonals is equal to two times the sum of the squares of sides of parallelogram.

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