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Rectangle: Shape and Properties

A special kind of parallelogram

A rectangle is a parallelogram whose sides intersect 90° angles.  Now, since a rectangle is a parallelogram, its opposite sides must be congruent.

 Example of a Rectangle   Rectangle Shape and Properties I. All angles are right angles.
    II. Opposite Sides are congruent (property of all parallelograms)
  • ML = NO
  • MNLO
III. Diagonals are Congruent
  • MOLN

  • Sides of Rectangle
    If side MN = 12 and side ML = 5, what is the length of the other two sides?
     Answer  

    Diagonals of Rectangle


    The diagonals of a rectangle are congruent.

    Proof of Diagnoals of Rectangle
    Triangle MLO is a right triangle, and  MO is its hypotenuse.By the pythagorean theorem, we know that
    The other half of the rectangle.
    If we divided the rectangle along diagonal NL, we would create triangle LNO. Since the opposite sides of a rectangle are congruent NO is 5 and lO is 12. Again, we can use the pythagorean theorem to find the hypotenuse, NL.


    As you can hopefully see, both diagonals equal 13, and the diagonals will always be congruent because the opposite sides of a rectangle are congruent allowing any rectangle to be divided along the diagonals into two triangles that have a congruent hypotenuse.

    Practice Problems

    Problem 1)
    Rectangle Practice Problem How Long is MO and MZ in the rectangle pictured on the left?
     Answer  
    Rectangles Diagonal Problem How Long is MO and MZ in the rectangle pictured on the left?
     Answer  

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