Let #bar(AB)# be cut into equal and unequal segments at #C and D# Show that the rectangle contained by #bar(AD)xxDB# together with the square on #CD# is equal to the square on #CB#?

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2 Answers
Oct 23, 2016

In the fig C is mid point of AB . So #AC=BC#

Now rectangle contained by #bar(AD) and bar(DB)# together with the square on#bar(CD)#

#=bar(AD)xxbar(DB)+bar(CD)^2#

#=(bar(AC)+bar(CD))xx(bar(BC)-bar(CD))+bar(CD)^2#

#=(bar(BC)+bar(CD))xx(bar(BC)-bar(CD))+bar(CD)^2#

#=bar(BC)^2-cancel(bar(CD)^2)+cancel(bar(CD)^2)#

#=bar(BC)^2->"Square on CB"# Proved