Question

if two altitudes of a triangle are equal, prove that it is an isosceles triangle​

Answer 1

GIVEN: In ∆ABC, Altitudes AD and BE are equal

TO PROVE :. AB=BC

PROOF :. In ∆BEC & ∆ADC  

BE=AD(GIVEN)

∠C =∠C (COMMON)

∠E = ∠D (EACH 90

∆BEC ≅ ∆ADC (AAS)                      .....(i)

Similarly, ∆BAE ≅ ∆ABD                 .....(ii)

Adding (I) & (ii)

∆BAC ≅ ∆ABC

AC = BC (By CPCT)

HENCE, PROVED ∆ABC is an isosceles triangle