ABCD is a parallelogram in which diagonals AC and BD intersect at O . if E, F, G ,H are mid points of AO, DO, CO ,BO respectively .then ratio of perimeter of quadrilateral EFGH to the perimeter of parallelogram ABCD.
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the triangles AOB and EOF are similar. => EF = AB / 2
the triangles FOG and BOC are similar. => FG = BC/2
the triangles GOH and COD are similar. => GH = CD / 2
the triangles HOE and DOA are similar. => HE = DA / 2
So the perimeter ratio = (EF+FG+GH+HE)/ (AB+BC+CD+DA)
= 1/2
the triangles FOG and BOC are similar. => FG = BC/2
the triangles GOH and COD are similar. => GH = CD / 2
the triangles HOE and DOA are similar. => HE = DA / 2
So the perimeter ratio = (EF+FG+GH+HE)/ (AB+BC+CD+DA)
= 1/2
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