Prove that medians of equilateral triangles are proportional to their corresponding sides.

In ΔABC and ΔDEF

Let  ΔABC and ΔDEF be similar triangle in which (AB,DE) (AC,DF) AND (BC,EF) ARE PAIR OF CORRESPONDING SIDES. Draw AL pependicular to BC and DM to EF.

∠ABL = ∠DEF

∠ALB = ∠DMF = 90°

∠BAL = ∠EDM  (since two angles are equal, third angle is also equal )

AL/DM = AB/DE = BL/EM  (corresponding sides are proportional in similar triangles )

But AB/DE = BC/EF (triangles are similar)

∴ AL/DM = BC/EF

HENCE PROVED

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