In a trapezium ABCD, AB | | DC and DC = 2AB. EF | | AB, where E and F

1.	In a trapezium ABCD, AB \| \| DC and DC = 2AB. EF \| \| AB, where E and F lie on BC and AD respectivelysuch thatDiagonal DB intersects EF at G. Prove that,BE 4EC 37EF-11AB.
Answer» given DC = 2 ABDraw BH parallel to AD. H will be the middle point of DC as AB = DH.Sin EF \|\| AB, FI = AB TheΔBHC andΔBIE are similar as the correspondingsides are parallel.So IE / HC = BE / BC IE = HC * BE / BC = y * 4x/7x = 4 y /7 EF = FI + IE= y + 4 y /7 = 11 y / 7 so 7 EF = 11 AB

In a trapezium ABCD, AB | | DC and DC = 2AB. EF | | AB, where E and F lie on BC and AD respectivelysuch thatDiagonal DB intersects EF at G. Prove that,BE 4EC 37EF-11AB.

Answer»

given DC = 2 ABDraw BH parallel to AD. H will be the middle point of DC as AB = DH.Sin EF || AB, FI = AB

TheΔBHC andΔBIE are similar as the correspondingsides are parallel.So IE / HC = BE / BC IE = HC * BE / BC = y * 4x/7x = 4 y /7

EF = FI + IE= y + 4 y /7 = 11 y / 7

so 7 EF = 11 AB