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rectangle

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

Rectangle angles In a rectangle, all angles are 90°

Diagonals of Rectangle

Rectangle angles 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

Problem 1)
In rectangle STAR below, SA =5, what is the length of RT?
Answer

Sides of Rectangle
Problem 2)
Sides of Rectangle
If side MN = 12 and side ML = 5, what is the length of the other two sides?
Answer
Problem 3)
Rectangle Practice Problem How Long is MO and MZ in the rectangle pictured on the left?
Answer
Challenge Problem) What is the value of x in rectangle STAR below?
Answer


SZT and SZA are supplementary angles, Therefore SZA is 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 ZSAcongruentZAS, being base angles of an isosceles triangle. Therefore, x = 30 °

challenge problem