Question

Two pillars AB and CD are standing on either side of the road as shown in the figure


If AF=CE ,then prove that BE=FD

Answer 1

The question in the attachment says "Two equal pillars" hence,

AB = CD

and given

AF = CE

Since they are pillars, they will be perpendicular to the ground.

Hence, by Pythagoras Theorem, BF will also be equal to ED


=> AB² + BF² = AF²

=> BF² = AF² - AB²

=> BF² = CE² - CD²

(since, AF = CE and AB = CD)

But CE² - CD² = ED²

=> BF² = ED²

=> BF = ED



Now subtract EF from both

BF = ED

=> BF - EF = ED - EF

=> BE = FD

(since, BF = EF + BE and ED = EF + FD)

Hence proved

Answer 2

Solution:-

Given :- AF = CE.

Now,

In Triangle ABF,

By Pythagoras Theorem,

AF^2 = AB^2 + BF^2

=> BF^2 = AF^2 - AB^2

=> BF^2 = CE^2 - CD^2 (AB = CD)____(1)

In Triangle CED,

By Pythagoras Theorem,

EC^2 = CD^2 + ED^2

=> ED^2 = EC^2 - CD^2.______(2)

From eq 1 and 2. we get,

BF^2 = ED^2

=> BF = ED

Now , Subtracting EF from both side.

=> BF - EF = ED - EF

=> BE = FD.

Hence, Proved.