Question

How to prove?

Answer 1

As below.

Explanation:

If the diagonals bisect each other at right angles, the quadrilateral should be a Rhombus or a Square.

In addition to the above, if the diagonals are equal, it's a Square and if unequal, it's a Rhombus.

A rhombus is basically a diamond, or a slanted, stretched square. ... A Rhombus always has four equal sides; a square always has four equal sides. A square always has four 90 degree angles. The angles of a rhombus can be any measure (each pair of opposite angles will be equal, and all four will always add up to 360).

`color(crimson)("The rhombus has the following properties:"`
`color(crimson)("All the properties of a parallelogram apply" \ "(the ones that matter here are parallel sides", \ "opposite angles are congruent, and consecutive angles are supplementary). "`
`color(crimson)("The diagonals bisect the angles. "`
`color(crimson)("The diagonals are perpendicular bisectors of each other."`