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ABC is an equilateral triangle, and AD and BE are perpendiculars to BC and AC respectively. Prove that:1. AD=BE2. BD=CE`[ DeltaABD=DeltaBCE.]` |
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Answer» We know perpendicular in an equilateral triangle are bisectors of opposite sides. `:. BD= DC = (BC)/2->(1)` `AE = CE = (AC)/2->(2)` As `AC = BC` `:. (BC)/2 =(AC)/2` `:. BD = CE` Now, in `Delta ABD` and `Delta BCE` `AB =BC` `BD = CE` `/_ADB =/_BEC=90^@` So, by `R.H.S. ` congruency rule, `Delta ABD ~= Delta BCE` `:. AD = BE` |
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