1.

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.]`

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`


Discussion

No Comment Found