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ABC is an equilateral triangle, and AD a...

ABC is an equilateral triangle, and AD and BE are perpendiculars to BC and AC respectively. Prove that: 1. AD=BE 2. BD=CE `[ DeltaABD=DeltaBCE.]`

Text Solution

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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`
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