AD and BE are the altitudes of an isoscles triangle ABC with AB = BC. Prove that AE = BD?

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AD and BE are the altitudes of an isoscles triangle ABC with AB = BC. Prove that AE = BD?

2006-11-22 02:58:13 · 2 answers · asked by Akilesh - Internet Undertaker 7 in Science & Mathematics ➔ Mathematics

2 answers

in triangles ABE and BEC
AB=BC (given)
therefore the triangles are congruent
therefore BD=EC
but EC=AE as in an isosceles triangle the altitude bisects the base
so BD=AE (cpct)
hence proved

2006-11-22 03:11:09 · answer #1 · answered by raj 7 · 0⤊ 0⤋

Name the intersection of the two altitudes R.Sorry, but this cannot be proven because it is false. It is easy to draw examples showing that BD > AE.

2006-11-22 12:05:15 · answer #2 · answered by ironduke8159 7 · 0⤊ 1⤋