In ∆ABC, BD ⊥ AC and CE ⊥ AB such that BE=CD. Prove that BD=CE.

Question

Philoid · Accepted Answer

It is given that,

BD is perpendicular to AC and CE is perpendicular to AB

Now, in ∆BDC and ∆CEB we have:

BE = CD (Given)

∠BEC = ∠CDB = 90^o

And, BC = BC (Common)

∴ By RHS congruence rule

∆BDC ≅ ∆CEB

BD = CE (By CPCT)

Hence, proved