In an isosceles triangle ABC with AB =AC , BD and CE are two medians . prove that BD = CE
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Answer:
T.P.T. (i) ∆ AEX ~ ADB
(ii) CA / AB = CE / DB
P.F. (i) In ∆ AEC and ∆ ADB
∠1 = ∠2 (each 90°)
∠A = ∠A (common)
∴ ∆ AEC ~ ∆ ADB (by AA rule)
(ii) ∆ AEC ~ ∆ ADB
CA / AB = CE / DB (∵ angles are similar)
∴ Corresponding sides are proportional) H.P.
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