Question

4. ABCD is a trapezium in which AB II DCBD is a diagonal and E is the mid-point of AD.
A line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). Show that
Fis the mid-point of BC.
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Answer 1

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Trapezium:

A quadrilateral in

which one pair of opposite sides are parallel is called a trapezium.

Converse

of mid point theorem:

The

line drawn through the midpoint of one side of a triangle, parallel to another

side bisect the third side.

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Given,

ABCD is a trapezium in which AB || DC, BD is a

diagonal and E is the mid-point of AD and a line is drawn through E parallel to

AB intersecting BC at F such that EF||AB.

To Show:

F is the mid-point of BC.

Proof:

Let EF

intersected BD at G.

In ΔABD,

E is the mid point of AD and also EG || AB.

we get, G is the mid point of BD

(by Converse of mid

point theorem)

Similarly,

In ΔBDC,

G is the mid point of BD and GF || AB || DC.

Thus, F is the mid point of BC

(by Converse of mid point theorem)

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Hope this will help you...