Question

In the equilateral triangle ABC, AD and BE are
the medians on the sides BC and CA
respectively. Show that AD = BE
​

Answer 1

Answer:

consider a equilateral triangle ABC, therfore AB=BC=AC AD and BE are the medians. therefore AD perpendicular AC , therefore AE=EC (median divides the line segment into two equal halves) similarly, BD=CD So considerring triangles ABE and ABD, AE=BD ( since the median divides two equal sides) angle EAB= angle EBA=60degrees. (each angle of an equilateral triangle is 60 degrees) AB=AB(common) therefore, triangle ABE congruent triangle ABD (SAS) so, AD=BE (C.P.C.T) Hence, proved

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