In order to prove that vertices of a quadrilateral form a square, I must do what?(2 points)

Question

Prove that the vertices form a
rectangle
by using one of the 4 methods we learned. Then prove that the vertices form a
rectangle
AND a
square
. This will prove that the vertices form a
rhombus
.

Answer 1

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

1. Prove it is a Rectangle: Show that the quadrilateral is a rectangle by using one of the four methods (e.g., proving that opposite sides are equal and parallel, showing that all angles are right angles, verifying the diagonals are equal in length, or demonstrating that adjacent sides are perpendicular).

2. Prove it is a Rhombus: Show that the quadrilateral is a rhombus by proving that all four sides are equal in length. This can be done using the distance formula to calculate the lengths of all four sides.

3. Conclude it is a Square: Since you have shown that the quadrilateral is both a rectangle (which has equal angles of 90 degrees) and a rhombus (which has all sides equal), you can conclude that the quadrilateral must be a square (as a square is defined as a quadrilateral that is both a rectangle and a rhombus).

By completing these steps, you can prove that the vertices of the quadrilateral form a square.