Rectangle: Shape and Properties

A special kind of parallelogram

A rectangle is a parallelogram with 4 right angles.  Now, since a rectangle is a parallelogram, its opposite sides must be congruent and it must satisfy all other properties of parallelograms

The Properties of a Rectangle

4 Right Angles

In a rectangle, all angles are 90°

Diagonals of Rectangle

The diagonals of a rectangle are congruent.

It's easy to prove that the diagonals of a rectangle with the Pythagorean theorem. Click here to see the proof.

Practice Problems

Since the diagonals of a rectangle are congruent, RT has the same length as SA.

Therefore, RT = 5

Side LO = 12 and NO = 5

Remember that a rectangle is a parallelogram, so it has all of the properties of parallelograms , including congruent opposite sides.

Finding length of MO

Since the diagonals of a rectangle are congruent MO = 26.

Finding length of MZ

To find MZ, you must  remember that the diagonals of a parallelogram bisect each other.(Remember a rectangle is a type of parallelogram so rectangles get all of the parallelogram properties)

If MO = 26 and the diagonals bisect each other, then MZ = ½(26) = 13

$$\angle SZT$$ and $$\angle SZA$$ are supplementary angles,
Therefore $$\angle SZA = 120°$$

Next, remember that the diagonals of any parallelogram bisect each other and the diagonals of a rectangle are congruent.

Therefore, SZ = AZ, making SZA isosceles and $$\angle$$ZSA$$\angle$$ZAS, being base angles of an isosceles triangle. Therefore, x = 30 °

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