Mathematics
In a quadrilateral ABCD, AD2 = AC2 - DC2
Show that ∠D = 90°.
Pythagoras Theorem
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Answer
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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