Question

Attached.

Answer 1

if it's equilateral it will be a square, so... true

Answer 2

Well....I know it's true. But why?

Answer 3

You can prove that diagonals of a square are perpendicular by using coordinates of the vertices and finding slopes of the lines that pass throu them

Answer 4

The short answer, "One property of a square is that its diagonals are perpendicular bisectors of each other"

The longer answer is a proof:

1) a diagonal of a square bisects the 90º angles of a square:
pf: by SSS, the two triangles are congruent, so corresponding angles a are equal
a+a= 90 so a= 45º
(See figure)


2) The 4 triangles formed by the diagonals are congruent by angle a, side, angle a
(See figure)

3) angle b created by the diagonals is 90º
pf: a+a+b=180. a=45, so 90+b=180 and b=90