Why are diagonals of a rhombus perpendicular

In a rhombus ABCD, prove that the diagonals are perpendicular to each other. To prove that two lines are perpendicular , when all we have are those two lines, we can use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.

Our diagonals intersect at point O, so we'd need to show the two linear angles formed at that intersection point are equal, and we can do that with triangle congruency. A rhombus is a parallelogram, so we will use what we already know about parallelograms - that the diagonals bisect each other. The converse of this is also true: if a parallelogram's diagonals are perpendicular, it is a rhombus. In particular, diagonals of a parallelogram intersect each other at a point that divides each diagonal in half.

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.

How do you prove that the diagonals of a rhombus are perpendicular? Geometry Quadrilaterals Quadrilaterals. Zor Shekhtman. Nov 16, Proof is below. Explanation: Rhombus is a parallelogram with all sides equal to each other. What is the ratio of the area Is a rhombus always a trapezoid?

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