Question

Show that the diagonals of a parallelogram divide
it into four triangles of equal area.
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Answer 1

Step-by-step explanation:

Each of the diagonals of a parallelogram divides it into two congruent triangles, as we saw when we proved properties like that the opposite sides are equal to each other or that the two pairs of opposite angles are congruent. Since those two triangles are congruent, their areas are equal.

We also saw that the diagonals of the parallelogram bisect each other, and so create two additional pairs of congruent triangles.

Now will go one step further, and relying on the fact that triangles with the same base and same height have equal areas, we will see that all four triangles created by the intersecting diagonals of a parallelogram have equal areas.

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.