The diagonals of a rhombus are perpendicular to each other theorem
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Answer
Proof is below.
Rhombus is a parallelogram with all sides equal to each other.
Therefore, rhombus has all the properties of parallelogram. In particular, diagonals of a parallelogram intersect each other at a point that divides each diagonal in half.
Therefore, assuming we have a rhombus ABCD with diagonals ACand BD intersecting at point O, triangles ΔABO and ΔCBO are congruent by three sides:
AB=CB as sides of a rhombus;
BO is shared by both triangles;
AO=CO as two halves of a diagonal AC.
From the congruence of these triangles follows that angles ∠AOBand ∠COB (lying opposite to equal sides AB and CB) are equal to each other and, therefore are equal to 90o.
As a more detailed description of all the properties of parallelograms and other geometrical objects with all the required proofs of each I can suggest to listen the lectures about this at UNIZOR by following the menu options Geometry - Quadrangles.
Answer:
Rhombus is a parallelogram with all sides equal with each other