How do you prove that the diagonals of a rhombus are perpendicular?
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.
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.
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To prove that the diagonals of a rhombus are perpendicular, we can use properties of rhombuses and basic geometry principles. Here's a stepbystep proof:

Definition of a Rhombus: A rhombus is a quadrilateral with all four sides of equal length.

Diagonals of a Rhombus: In a rhombus, the diagonals bisect each other at right angles.

Draw the Rhombus: Start by drawing a rhombus. Label the vertices as A, B, C, and D.

Diagonals Bisect Each Other: Draw the diagonals AC and BD. These diagonals intersect at point O, the point of intersection.

Diagonals are Equal: Because a rhombus has all sides equal, it follows that AC = BD.

Opposite Sides of a Rhombus are Equal: By the definition of a rhombus, opposite sides are equal. So, AB = BC = CD = DA.

Triangles in a Rhombus: Triangles AOB, BOC, COD, and DOA are congruent by the SideSideSide (SSS) criterion, as they have two sides equal (AO = BO, BO = CO, CO = DO, and DO = AO) and the included angle between them is 90 degrees (angle AOB, angle BOC, angle COD, and angle DOA).

Congruent Triangles: Since triangles AOB, BOC, COD, and DOA are congruent, their corresponding angles are equal. Therefore, angle AOB = angle BOC = angle COD = angle DOA.

Opposite Angles of a Parallelogram: In a parallelogram, opposite angles are equal.

Conclusion: Since angle AOB and angle COD are opposite angles in parallelogram ABCD, and they are also corresponding angles of congruent triangles, they must be equal. Similarly, angle BOC and angle DOA are equal.

Perpendicular Diagonals: Since angles AOB and COD are equal and angle AOB = angle COD = 90 degrees (since the diagonals bisect each other at right angles), it follows that the diagonals AC and BD are perpendicular.
Therefore, we have proved that the diagonals of a rhombus are perpendicular.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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