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ABC is an isosceles triangle with AB=AC. D,E and F are midpoints of the sides BC,AB and AC respectively.Prove that the line segment AD is perpendicular to EF and is bisected by it.

Asked by laxmi.agarwal055 21st February 2018, 7:02 PM
Answered by Expert
begin mathsize 16px style let space AD space and space EF thin space intersect space at space straight O
now space in space increment ABD space and space increment ACD
AB equals AC
so space angle ADB equals angle ADC equals 90 degree

angle BAD equals angle CAD
so space in space increment EAO space and space increment FAO
angle EAO equals angle FAO
also space AE equals AF
AO space common
so space by space SAS space triangles space are space congruent
so space angle EOA equals angle FOA equals 90........... space linear space pair space left parenthesis cpct right parenthesis
EO equals FO space.... cpct end style
Answered by Expert 22nd February 2018, 4:27 PM
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