Question

show that the diagonals of a parlellogram divides it into 4 triangles of equal area ​

Answer 1

ABCD is a parallelogram with diagonals AC and BD which intersect at point O. Show that all four triangles created by these diagonals – ΔAOD, ΔCOD, ΔAOB and ΔCOB – have equal areas.We already know that the opposite pairs of triangles (ΔAOD≅ ΔCOB; ΔAOB≅ ΔCOD) are congruent, and thus have equal areas. So if we can show that one of the other pairs also has equal areas, all four will be equal When comparing the ratio of areas of triangles, we often look for an equal base or an equal height – in this case, we have both: Since the diagonals bisect each other, AO=OC, and both ΔCOB and ΔAOB share the same height – BE.

intersecting diagonals with height

So their areas are equal, and so all four areas are equal

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