In a quadrilateral ABCD- ang-B - 90 deg- AD2 - AB2 - BC2 - CD2- prove that ang-ACD - 90 deg-

In order to prove angle it is enough to prove that .Given, nbsp; nbsp; .....(1)Since, so applying Pythagoras theorem in the right angled triangle ABC, we ...

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Standard X

Mathematics

Pythagoras Theorem

In a quadrila...

Question

In a quadrilateral ABCD, ∠B = 90°, AD² = AB² + BC² + CD², prove that ∠ACD = 90°.

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Solution

In order to prove angle it is enough to prove that .
Given,

.....(1)
Since, so applying Pythagoras theorem in the right angled triangle ABC, we get
.....(2)
From (1) and (2), we get

Therefore, angle . (Converse of pythagoras theorem)

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In a quadrilateral ABCD, ∠B = 90°, AD2 = AB2 + BC2 + CD2, prove that ∠ACD = 90°.

In order to prove angle it is enough to prove that .Given, .....(1)Since, so applying Pythagoras theorem in the right angled triangle ABC, we get .....(2)From (1) and (2), we get Therefore, angle . (Converse of pythagoras theorem)

In a quadrilateral ABCD, ∠B = 90°, AD² = AB² + BC² + CD², prove that ∠ACD = 90°.

In order to prove angle it is enough to prove that .
Given,

.....(1)
Since, so applying Pythagoras theorem in the right angled triangle ABC, we get
.....(2)
From (1) and (2), we get

Therefore, angle . (Converse of pythagoras theorem)