Q6 of 24 Page 21

Are the two diagonals of a rectangle equal? Why?


A rectangle is a parallelogram where each angle is a right angle.


Here, AD = BC …(eq)1


And AB = CD


According to Pythagoras theorem,


(Hypotenuse)2 = (one side)2 + (other side)2


In Δ ABD,


Hypotenuse = BD


One side = AB


And other side = AD


∴ (BD)2 = (AB)2 + (AD)2 …(eq)2


In Δ ABC,


Hypotenuse = AC


One side = AB


And other side = BC


∴ (AC)2 = (AB)2 + (BC)2


= (AB)2 + (AD)2 …(eq)3 …(from eq1)


As is clear from (eq)2 and (eq)3


BD2 = AC2


Taking square root on both sides,


BD = AC


∴ Diagonals of a rectangle are equal.


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