Question

BD and CE are two altitudes of △ABC such that BD=CE Prove that△ABC is isosceles.

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Answer 1

Answer: Given:-

BD and CE are two altitudes of △ABC, BD=CE To prove:- △ABC is isosceles Proof:- In △ECB and △DBC

                 ∵ EC      = BD (Given)

                    ∠BEC = ∠BDC (BD and CE are altitudes)

                     BC      = BC (Common side)                  

                 ∴ △ECB ≅ △DBC(RHS congruency rule)

                    ∠B      =  ∠C      (By CPCT)                  

                    ∵ ∠B      =  ∠C

                     ∴ AB      =  AC (sides opposite to equal angles are equal)

 Hence, △ABC is a isosceles triangle.