To prove: The sum of the lengths of the sides of a parallelogram is equal to the sum of the squares of the lengths of its diagonals.
Explanation of Solution
Given information: The points are
Formula used:
Proof: Apply the formula to sides lengths between the given points,
Similarly,
Hence, the sum of the square of the sides,
Now, calculate the diagonals length,
Hence, the sum of the squares of the diagonals,
Hence, the sum of the lengths of the sides of a parallelogram is equal to the sum of the squares of the lengths of its diagonals.
Hence, proved.
Chapter 9 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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