Mathematics
Prove that the line segment joining the mid-points of a pair of opposite sides of a parallelogram divides it into two equal parallelograms.
Theorems on Area
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Answer
Let us consider ABCD be a parallelogram in which E and F are mid-points of AB and CD. Join EF.
Let us construct DG ⊥ AB and let DG = h, where h is the altitude on side AB.
Area of ||gm ABCD = base × height = AB × h
Area of ||gm AEFD = AE × h = × h …….(i) [Since E is the mid-point of AB]
Area of ||gm EBCF = EB × h = × h …….(ii) [Since E is the mid-point of AB]
From (i) and (ii)
Area of ||gm AEFD = Area of ||gm EBCF.
Hence proved, that the line segment joining the mid-points of a pair of opposite sides of a parallelogram divides it into two equal parallelograms.
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