Q16 of 24 Page 157

In the triangle ACB, the medians BE and CF intersects at the point G. The midpoints of BG and CG are P and Q respectively. If PQ = 3 cm, then let us write the length of BC.


In ΔABC, as F is midpoint of AB and E is midpoint of AC, 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 EF||BC


Similarly, In ΔOBC, as P is midpoint of BG and Q is midpoint of GC, 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 PQ||BC


⇒ BC = 2× PQ


⇒ BC = 2 × 3


⇒ BC = 6 cm


∴ The length of BC is 6 cm.


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