In the adjoining figure, ∆ABC is an isosceles triangle in which AB = AC. If E and F be the midpoints of AC and AB respectively, prove that BE = CF.

Figure

Given:ABC is an isosceles triangle in which AB=AC.E and F are midpoints of AC and AB, respectively.To prove:BE=CFProof:E and F are midpoints of AC and AB, respectively.=>AF=FB, AE=ECAB=AC=>12AB=12AC=>FB=ECABC=ACB       (angle opposite to equal sides are equal )=>FBC=ECBConsider BCF and CBE:BC=BC                  (common)FBC=ECB      (proved above)FB=EC                   (proved above)By SAS congruence property:BCF  CBEBE =CF        (corresponding parts of the congruent triangles)

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