Q10 of 24 Page 157

In the triangle ABC, AD is median. From the points B and C, two straight lines BR and CT, parallel to AD are drawn, which meet extended BA and CA at the points T and R respectively. Let us prove that


Since it is given that AD is the median to side BC,


⇒ D is midpoint to BC


Also, it is given that AD||CT||BR, so by applying theorem:-


Through the mid-point of any side, if a line segment is drawn parallel to second side, then it will bisect the third side and the line segment intercepted by the two sides of the triangle is equal to half of the second side.



⇒ TC = RB ……… (1)


As , it can also be written as,



Using equation (1) in above equation,



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