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CBSE Class 9 Answered

Diagonals of a parallelogram intersect each other at point O If AO=5,BO=12 and AB=13 then show that quadrilateral ABCD is a rhombus
Asked by Rajeshparve | 25 Oct, 2018, 10:40: PM
Expert Answer
 
Consider triangle AOB,
AO = 5 cm, BO = 12 cm
AO2 + BO2 = 52 + 122 
                 = 25 + 144
                 = 169
                 = 132 
As, AO2 + BO2 = AB2 
Hence, using converse of Pt=ythagoras theorem triangle AOB is right angle triangle.
So, diagonals are perpendicular to each other. Hence, ABCD is a rhombus.
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