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 | 25th 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.

Answered by Sneha shidid | 26th Oct, 2018, 10:08: AM