AMSCO'S Geometry. New York - Rye High School

The Square 39910-6 THE SQUAREDEFINITIONA square is a rectangle that has two congruent consecutive sides.If consecutive sides AB and AD of rectangle ABCD are congruent (that is,if AB > AD), then rectangle ABCD is a square.Theorem 10.17A square is an equilateral quadrilateral.Given ABCD is a square with AB > BC.DCProveAB > BC > CD > DAProofA square is a rectangle and a rectangle is a parallelogram,so ABCD is a parallelogram. It is given thatAB > BC. Opposite sides of a parallelogram are congruent,so AB > CD and BC > DA. Using the transitiveproperty of congruence, AB > BC > CD > DA.ABTheorem 10.18A square is a rhombus.GivenSquare ABCDProveABCD is a rhombus.ProofA square is an equilateral quadrilateral. If a quadrilateral is equilateral,then it is a rhombus. Therefore, ABCD is a rhombus.Properties of a Square1. A square has all the properties of a rectangle.2. A square has all the properties of a rhombus.Methods of Proving That a Quadrilateral Is aSquareWe prove that a quadrilateral is a square by showing that it has the special propertiesof a square.