prove that the 4 triangles into which the diagonals of a rhombus divide it are congruent

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Solution

Let there be a rhombus ABCD in which O is the mid point where the diagonals intersect
Since the diagonals of a rhombus intersect each other AO = OC and BO = OD
Also in the rhombus all sides are equal
hence all the four triangles formed are congruent by SSS congruence.

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