Rd sharma

Asked by AkshayPathak12 | 11th Jul, 2010, 09:28: PM

Expert Answer:

Dear Student,
 
Let ABC be the triangle, with D and E as mid points of AB and AC respectively.
So, DE is parallel to BC.
Now,
In triangles ADE and ABC
 Angle A is common
angle ADE = angle ABC
AND
angle AED =angle ACB
Hence triangles ADE and ABC are similar triangles by AAA property.
So all their sides must be in same ratio!
As, AD: AB = AE:AC = 1:2
=> DE:BC = 1:2
=> DE = (BC)/2
Hence Proved.
 
Regards Topperlearning.
 

Answered by  | 14th Jul, 2010, 02:38: PM

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