Question

Two equal pillars AB and CD are standing on the either side of the road as shown in the figure.
If AF = CE, then prove that BE = FD.

Answer 1

hey dear your answer is here..

here
AB = CD
AF = CE
angle B = angle D

so bye SSA both triangle ABF and CDE are congruent.

by cpct
BF = ED
BF - EF = ED - EF
BE=FD

Answer 2

From the figure, you will find out two similar triangles i.e. △ABF = △CDE.

In these two triangles, you will also discover ∠B =∠D = 90°, side AF – side CE, and side AB = side CD.

According to the RHS rule, △ABF = △CDE are concurrent. As per CPCT (Corresponding parts of congruent triangles), side BF = side DE.

When you subtract common length EF from both sides, we obtain => BF – EF = DE – EF => BE – FD.

Hence, it is proved.