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7. Prove that the sum of …

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7. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of squares of its diagonals.

Posted by Atul Kumar 5 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 5 years, 3 months ago

Given: ABCD is a rhombus

To prove: AB² + BC²+ CD²+ AD² = AC² + BD²

Proof:

We know, diagonals of a rhombus bisect at right angles.

Therefore, from triangle AOB,

AB² = AO²+ OB²

4AB² = AC² + BD²

Thus, AB² + BC² + CD² + DA² = 4AB² = AC² + BD²

[As AB = BC = CD = DA]

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