Ex 8.2, 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. Show that F is the mid-point of BC.
Given: ABCD is a trapezium where
AB ∥ DC
E is the mid point of AD, i.e., AE = DE
& EF ∥ AB
To prove: F is mid point of BC , i.e., BF = CF
Proof: Let EF intersect DB at G.
In ∆ ABD
E is the mid-point of AD.
and EG ∥ AB
∴ G will be the mid-point of DB.
Given EF ∥ AB and AB ∥ CD,
∴ EF ∥ CD
In ΔBCD,
G is the mid-point of side BD.
& GF ∥ CD
∴ F is the mid-point of BC.
Hence proved

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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