Question

In the figure, ABCD is a trapezium in which AB || DC. E and F are the mid-points
of AD and BC respectively. DF and AB are produced to meet at G. Also AC and EF
intersect at the point O. Show that
(i) EO || AB
(ii) AO = CO




​

Answer 1

Step-by-step explanation:

ABCD is the given trapezium.

It is given that E and F are the mid-point of the sides AD and BC respectively.

(i) Consider a △ADG,

By the converse of midpoint theorem,

EF∥AG and EF=

2

1

AG

⇒ EO∥AG

⇒ EO∥AB

(ii) Consider a △ADC

EO∥AB and AB∥DC

⇒ EO∥DC

And we know that E is the midpoint of AD.

Thus, by basic proportionality theorem, we have, O is the mid-point of AC

∴ AO=CO

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