if a line is parallel to base of trapezium and bisect one of the non parallel sides, then prove that it bisect either diagonal of the trapezium
plz answer with fig.
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Given: ABCD is a trapezium. EF is parallel to DC. and it bisects one of the non parallel sides.
TPT: EF bisects either of the diagonals of the trapezium
proof:
let EF bisects AD, i.e. E is the mid-point of AD.
now in the triangle ADC,
E is the mid-point of AD and
EM PARALLEL DC (because e.g. parallel dc)
from the converse of the mid point theorem: the straight line drawn through the mid-point of one side of a triangle parallel to another , bisects the third side.
therefore M is the mid point of AC.
thus if EF bisects AD at E , it also bisects the diagonal AC.
similarly we can show that if EF bisects BD at F , it also bisects the diagonal BD.
hope this helps you.
tanay1438:
plz give me fig. that will help me more
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