Q16 of 24 Page 157

In the triangle ABC, D is any point on the side AC. The midpoints of AB, BC, AD and DC are P, Q, X, Y respectively. If PX = 5 cm, then let us write the length of the side QY.


In ΔABD, as X is midpoint of AD and P is midpoint of AB, 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 PX parallel to BD


⇒ BD = 2 × PX = 10 cm


Similarly, In ΔBDC, as Y is midpoint of DC and Q 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 QY is parallel to BD


⇒ QY = 5 cm


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