The diagonals of arhombus are perpendicular bisectors of each other. Proof this property
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Proof that the diagonals of a rhombus are perpendicular
Corresponding parts of congruent triangles are congruent, so all 4 angles (the ones in the middle) are congruent. This leads to the fact that they are all equal to 90 degrees, and the diagonals are perpendicular to each other.
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