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Mathematics

In a quadrilateral ABCD, AD2 = AC2 - DC2

Show that ∠D = 90°.

Pythagoras Theorem

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Answer

In a quadrilateral ABCD, AD. Distance Formula, Concise Mathematics Solutions ICSE Class 9.

ABCD is a quadrilateral, join diagonal AC.

Given,

AD2 = AC2 - DC2

⇒ AD2 + DC2 = AC2

In △ADC:

AD and DC are two sides

AC is the longest side

By applying converse of pythagoras theorem,

If in a triangle,

(side 1)2 + (side 2)2 = (longest side)2

then the triangle is right-angled.

∴ Triangle ADC is a right-angled at D.

So, ∠D = 90°

Hence proved that ∠D = 90°.

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