Q5 of 109 Page 314

In the adjoining figure, and are the medians of and Show that

Here in AD and BE are medians.


Hence, in ∆ABC, we have:
AC = AE + EC


But AE = EC … as E is midpoint of AC


∴ AC = 2EC …(1)


Now in ∆BEC,


DF || BE


Also, EF = CF … by midpoint theorem, as D is the midpoint of BC


But,


EC = EF + CF


∴ EC = 2 CF …(2)


From 1 and 2, we get,


AC = 4 CF


∴


More from this chapter

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In the adjoining figure, is a trapezium in which and are the midpoints of and respectively. and when produced meet at Also, and intersect at Prove that (i) (ii) (iii)

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In the adjoining figure, is a median of and Show that is also a median of

6

In the adjoining figure, is a parallelogram. is the midpoint of and through a line segment is drawn parallel to to meet produced at and it cuts at Prove that

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7

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