Q16 of 24 Page 157

In the triangle ABC, the midpoint of BC, CA and AB are D, E and F respectively; FE intersects AD at the point O. If AD = 6 cm, let us write the length of AO.


In ΔABC, as F is midpoint of AB and D is midpoint of BC, we apply the theorem:-


The line segment joining the midpoints of two side of a triangle is parallel to the third side and equal to half of it, we get


and FD|| AC


Also, it is given that E is the midpoint of AC



From above two equations, we get, AE = FD


In ΔFOD and ΔEOA,


∠FOD = ∠EOA (Opposite angles)


∠FDO = ∠EAO (Alternate Interior angles as FD || AE)


Also, ∠OFD = ∠OEA (Alternate Interior angles as FD || AE)


⇒ ΔFOD ≅ ΔEOA


∴ AO = OD




∴ The length of AO is 3 cm.


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