Question

"Question 4 ABCD is a trapezium in which AB || DC, BD 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 the given figure). Show that F is the mid-point of BC.

Class 9 - Math - Quadrilaterals Page 150"

Answer 1

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.

========================================================

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)

_____________________________________________________________

 Hope this will help you...

Answer 2

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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.

========================================================

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)

_____________________________________________________________

 Hope this will help you...