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

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.