AMSCO'S Geometry. New York - Rye High School

The Rectangle 38910-4 THE RECTANGLEDEFINITIONA rectangle is a parallelogram containing one right angle.If one angle, A, of a parallelogram ABCD is a right angle, then ~ABCDis a rectangle.Any side of a rectangle may be called the base of the rectangle. Thus, if sideAB is taken as the base, then either consecutive side, AD or BC, is called thealtitude of the rectangle.Since a rectangle is a special kind of parallelogram, a rectangle has all theproperties of a parallelogram. In addition, we can prove two special propertiesfor the rectangle.Theorem 10.8All angles of a rectangle are right angles.GivenRectangle ABCD with A a right angle.DCProveProofB, C, and D are right angles.By definition, rectangle ABCD is a parallelogram. Opposite angles of a parallelogramare congruent, so A C. Angle A is a right angle so C is a rightangle. Consecutive angles of a parallelogram are supplementary. Therefore,since A and B are supplementary and A is right angle, B is also a rightangle. Similarly, since C and D are supplementary and C is a right angle,D is also a right angle.ABTheorem 10.9The diagonals of a rectangle are congruent.GivenABCD is a rectangle.DCProveAC > BDStrategyProve DAB CBA.ABThe proof of Theorem 10.9 is left to the student. (See exercise 12.)