Question

can we prove a quadrilateral a square by slope method and how?​

Answer 1

There are four methods that you can use to prove that a quadrilateral is a square. In the last three of these methods, you first have to prove (or be given) that the quadrilateral is a rectangle, rhombus, or both:

If a quadrilateral has four congruent sides and four right angles, then it’s a square (reverse of the square definition).

If two consecutive sides of a rectangle are congruent, then it’s a square (neither the reverse of the definition nor the converse of a property).

If a rhombus contains a right angle, then it’s a square (neither the reverse of the definition nor the converse of a property).

If a quadrilateral is both a rectangle and a rhombus, then it’s a square (neither the reverse of the definition nor the converse of a property).