In a trapezium ABCD, AB is parallel to DC and DC = 2AB E is point on BC such that BE : EC = 3:4. EF is drawn parallel to AB where F is a point on AD . Prove that 7EF = 10AB.

ABCD is a trapezium. where . and

DC = 2 AB .......(1) and BE : EC = 3:4.............(2)

from eq(2):

the triangles CGE and triangles CAB are similar triangles.

therefore ratio of corresponding sides are equal.

since , therefore

the triangles AFG and ADC are similar triangles.

therefore

from eq(1):

adding eq(3) and eq(4):

which is the required result.

hope this helps you.

cheers!!

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