Question

In a quadrilateral ABCD, ∠B = 90° and ∠D = 90°. Prove that :
2AC² - AB² = BC² + CD² + DA²

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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given :-

In a quadrilateral ABCD, ∠B = 90° and ∠D = 90°.

To Prove :-

2AC² - AB² = BC² + CD² + DA²

Solution :-

In △ABC , using pythagoras theorem

➞ AC² = AB² + BC²

➞ AB² = AC² - B²__( i )

In △ADC, using pythagoras theorem

➞AC² = AD² + DC²__ ( ii )

LHS = 2AC² - AB²

➞ 2AC² - (AC² - BC²) __from ( i )

➞ 2AC² - AC² + BC²

➞ AC² + BC²

➞ AD² + DC² + BC²__from ( ii )

LHS = RHS Hence Proved.

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