In a quadrilateral ABCD d=90°.prove that 2ACsquare -bc square =ab square +ad square+dc square
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Step-by-step explanation:
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Given ∠B=∠D=90
∘
So ΔABC and ΔADC are right triangles.
In ΔABC,
AC
2
=AD
2
+BC
2
...(i) [Pythagoras theorem]
ΔADC,
AC
2
=AD
2
+DC
2
...(ii) [Pythagoras theorem]
Adding (i) and (ii)
2AC
2
=AB
2
+BC
2
+AD
2
+DC
2
∴2AC
2
−BC
2
=AB
2
+AD
2
+DC
2
Hence proved.
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