
This Page:
 Diagonal Related:
 Properties of parallelograms
 Is a square a rectangle?
 square
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

This Page:
 Diagonal Related:
 Properties of parallelograms
 Is a square a rectangle?
 square
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.
Since the diagonals of a rectangle are congruent MO = 26.
Finding length of MZTo 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 °