Question

In figure, BD and CE are altitudes. If BE = CD, prove that BD = CE

Answer 1

In triangle BEC and triangle CDB

angle BEC = angle CDB (right angle)

BE = CD. (given)

BC = BC (common hypotenuse)

Now triangle BEC is congruent to triangle CDB

Therefore it is proved that

BD = EC

Answer 2

In Δ BEC and ΔCDB

BE = CD .                                          (Given)

∠CDB =∠BEC                                   (Each of 90°)

BC = BC                                            (Common)

So,

By using SAS criterion,

Δ BEC ≅ ΔCDB

So,

By Corresponding parts of Congruent triangles (CPCT),

We get,

BD = CE

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Hence Proved