in order to prove that vertices of a quadrilateral form a square, I must do what?

Question

prove that the vertices form a_______(square, rectangle, quadrilateral, parallelogram, rhombus) by using one of the 4 methods we learned. Then prove that the vertices form a _____(square, rectangle, quadrilateral, parallelogram, rhombus) AND a_____(square, rectangle, quadrilateral, parallelogram, rhombus). This will prove that the vertices form a ___(square, rectangle, quadrilateral, parallelogram, rhombus)

Answer 1

To prove that the vertices of a quadrilateral form a square, you can follow these steps:

1. Prove that the vertices form a quadrilateral (which is usually taken as the initial step, as you already have four points).

2. Then prove that the vertices form a rectangle AND a rhombus. This is because a square is defined as a shape that is both a rectangle (all angles are 90 degrees) and a rhombus (all sides are equal).

3. This will prove that the vertices form a square.

So the completed steps would be:

1. Prove that the vertices form a quadrilateral.
2. Then prove that the vertices form a rectangle AND a rhombus.
3. This will prove that the vertices form a square.

You can use various methods such as distance formula for sides, slopes for angles, or diagonals for diagonality to prove these properties.