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Rectangle: Shape and PropertiesA 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 and it must satisfy all other properties of parallelograms .
Example of a Rectangle
All angles are right angles.
If side MN = 12 and side ML = 5, what is the length of the other two sides? Answer Side LO=12 and NO = 5 Diagonals of RectangleThe diagonals of a rectangle are congruent.
 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)
How Long is MO and MZ in the rectangle pictured on the left?
Answer Since diagonals of a rectangle are congruent MO = 26. To find MZ, you must remember a property of all parallellograms. Namely that the diagonals of a parallelogram bisect each other. Since a rectangle is a type of parallelogram, MZ = 13 
How Long is MO and MZ in the rectangle pictured on the left?
Answer Remember that opposite sides of a rectangle are congruent and that the diagonals of any parallelogram bisect each other. Lastly, the diagonals of a rectangle are congruent Top |
