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 (Figure). Prove that F is the mid-point of BC.

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Solution

Given line EF is parallel to AB and AB | | DC.
EF | | AB | | DC.
According to the converse of the mid-point theorem, in $Δ A B D$ , E is the mid-point of AD and EP is parallel to AB. [As EF | | AB]
By converse of mid-point theorem.
P is the mid-point of side BD.
Now, in $Δ B C D,$ P is mid-point of BD and, PF is parallel to DC. [AS EF | | DC]
By converse of mid-point theorem.
F is the mid-point of BC
Hence Proved.

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Q. 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.

A B C D

is a trapezium in which

A B ∥ D C, B D

is a diagonal and

E

is the mid-point of them. A line is drawn through

E

parallel to

A B

intersecting

B C

and

F

. Then

F

is the mid-point of

B C

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