Parallelograms


   
 
Theorem 4
 
Recall that the diagonals of a parallelogram bisect each other. Since a rectangle is also a parallelogram, the diagonals of a rectangle also bisect each other.
 
What is the additional property of the diagonals of a rectangle?
 
 
Let us draw a rectangle and measure its diagonals.
 
By measurement, you will find that
 
diagonal AC=diagonal BD
 
Let us prove this logically.
 
Statement
The diagonals of a rectangle are equal in length.
 
 
Given:
 
ABCD is a rectangle.
 
AC and BD are diagonals.
 
To prove:
 
AC=BD
 
Proof:
 
 
 
 
 
Now in triangles, ABD and ABC,
 
AB=AB (common side)
 
 
(each angle is a right angle)
 
 
AD=BC (opposite sides of parallelogram)
 
 
 
BD=AC (corresponding parts of
 
corresponding triangles)
 
Hence the theorem is proved.
 
 
     
   
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