If a quadrilateral is equilateral, its diagonals are perpendicular. True or false? Why?

Question

If a quadrilateral is equilateral, its diagonals are perpendicular. True or false? Why?

Answer 1

If a quadrilateral is equilateral it is rhombus. let there be rhombus ABCD.

AB = BC = CD = AD

with diagonals AC & BD

let X be the intersection of diagonals

there is isosceles triangle ABC, with BX perpendicular to AC (prove this by congruence theorems on your own), BD is extension of BX so AC is perpendicular to BD.

Answer 2

If a quadrilateral is equilateral it is either a rhombus or a square, which in both cases have diagonals that are perpendicular.