Question

N trapezium abcd, ab is parallel to dc and dc=2ab, ef drawn parallel to ab cuts ad in f and bc in e such that be:ec=3:4. diagonal db intersects ef at g. prove that 7ef=10ab.

Answer 1

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student-name Vidula Chhabra asked in Math
In a trapezium ABCD, AB ll CD and CD=2AB. EF is drawn parallel to AB cuts AD in F and BC in E such that BE / BC = 3/4. Diagonal DB intersects EF at G . Prove that 7 EF=10 AB.

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student-name Aakash Sharma answered this
14371 helpful votes in Math, Class XI-Science


Given : ABCD is a trapezium with AB || CD and CD = 2 AB

and EF || AB || CD with

and EF intersect BD at G.

Now,

In ΔBCD

GE || CD



and In ΔABD



So, EF = EG + FG



Hence 7EF = 10AB

Answer 2

Two Triangles are said to be similar if their i)corresponding angles are equal and ii)corresponding sides are proportional.(the ratio between the lengths of corresponding sides are equal)

•Similarity of triangles should be expressed symbolically using correct correspondence of their vertices

•AA similarity: if two angles of one triangle are respectively equal to two angles of another triangle then the two Triangles are similar.

•Any line parallel to the parallel sides of a Trapezium divides the non parallel sides proportionally.

SOLUTION IS IN THE ATTACHMENT.

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