Question

in given figure AB and CD are perpendiculars on BD. Also AB=CD and AF=CE . prove that BE=FD​

Answer 1

Answer:

Given -

AB and CD are perpendicular on BD

So angle ABF and angle CDE = 90°

AB = CD and AF = CE

Solve -

In triangle ABF and triangle CDE

AB = CD (given)

AF = CE (given)

angle ABF = CDE (90°)

so triangle ABF ≈ triangle CDE

according to this BF = DE ( byC.P.C.T.)

I hope it helps u

Answer 2

Answer:

Given: In ΔABF and ΔCDE,

AB ⊥ BD and CD⊥BD in which AB = CD and AF = CE

To prove: BE = FD

Proof: In ΔABF and ΔCDE,

         AB = CD

         AF=CE

         ∠ABF = ∠CDE = 90°

         ΔABF ≅ ΔCDE [By RHS Congruence Criteria]

         BF = DE [By CPCT]

         BF - EF = ED - EF [Subtract both the sides from EF]

         BE = FD

         Hence Proved.