CK12 - Geometry

So,. In this example,the diagonalsare congruent.Are the diagonalsof rectangles
alwayscongruent?The answeris yes.

Theorem:The diagonalsof a rectangleare congruent

The proofof this theoremrelieson the definitionof a rectangle(a quadrilateralin whichall anglesare con-
gruent)as well as the propertythat rectanglesare parallelograms.

• Given:Rectangle


• Prove:

Statement Reason

1. is a rectangle 1. Given


2. 
   
   
   
   2. Definitionof a rectangle
   
   
   
   


3. 
   
   
   
   3. Oppositesidesof a parallelogramare
   
   
   
   


4. 
   
   
   
   4. ReflexivePropertyof
   
   
   5. SAS CongruencePostulate
   
   
   
   


5. 
   
   
   
   6. Definitionof congruenttriangles(correspond-
      ing partsof congruenttrianglesare congruent)
   
   
   
   

6.

PerpendicularDiagonalsin Rhombi

Rememberthat rhombiare quadrilateralsthat havefour congruentsides.Theydon’tnecessarilyhaveright
angles(like squares),but they are also parallelograms.Also,all squaresare parallelograms.