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प्रश्न
Show that:
A diagonal divides a parallelogram into two triangles of equal area.
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उत्तर
Suppose ABCD is a parallelogram ...(given)
Consider the triangles ABC and ADC:
AB = CD ......[ABCD is a parallelogram]
AD = BC ......[ABCD is a parallelogram]
AC = AC .....[Common]
By Side- Side -Side criterion of congruence, we have,
ΔABC ≅ ΔADC
Area of congruent triangles are equal.
Therefore, Area of ABC = Area of ADC
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संबंधित प्रश्न
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Prove that: Area of ABC = Area of // gm BDEC.
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(i) 2 Area (POS) = Area (// gm PMLS)
(ii) Area (POS) + Area (QOR) = Area (// gm PQRS)
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In the given figure, the diagonals AC and BD intersect at point O. If OB = OD and AB//DC,
show that:
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(iii) ABCD is a parallelogram.
E, F, G, and H are the midpoints of the sides of a parallelogram ABCD.
Show that the area of quadrilateral EFGH is half of the area of parallelogram ABCD.
In parallelogram ABCD, E is a point in AB and DE meets diagonal AC at point F. If DF: FE = 5:3 and area of ΔADF is 60 cm2; find
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(iii) also, find the area of parallelogram ABCD.
