Mathematics
In the quadrilateral given below, AB || DC || EG. If E is mid-point of AD, prove that
(i) G is midpoint of BC
(ii) 2EG = AB + CD
Mid-point Theorem
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Answer
(i) Given,
EG || AB, we can say that
⇒ EF || AB
In △DAB,
E is midpoint of AD and EF || AB
∴ F is midpoint of BD (By converse of mid-point theorem).
EF = AB …….(1)
Given,
EG || DC we can say that,
FG || DC
In △BCD,
F is midpoint of BD and FG || DC
∴ G is midpoint of BC (By converse of mid-point theorem).
Hence, proved that G is midpoint of BC.
(ii) In △BCD,
F is midpoint of BD and G is midpoint of BC
∴ FG = DC …….(2)
Adding eqn. 1 from part (i) and eqn. 2 we get,
EF + FG = AB + DC
EG = (AB + CD)
2EG = AB + CD.
Hence, proved that 2EG = AB + CD.
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