Quadrilaterals and Polygons: Squares, Rectangles and Rhombi

Properties of Special Parallelograms: Rectangles

 

A rectangle is a special parallelogram with the following properties:

• All four angles are congruent and measure 90°

• Diagonals are congruent

 

Keep in mind that since a rectangle is a parallelogram, it also has all the properties we learned about parallelograms.

Let’s look at a rectangle ABCD and see how the properties can be applied.

rectangle ABCD with diagonals intersecting at point O

 

Example 1

If angle ABD measures (3x + 4)° and angle CBD measures (5x – 12)°, find the value of x.

One property of rectangles is that all four angles measure 90°.

(3x + 4) + (5x – 10) = 90

8x – 6 = 90

8x = 96 x = 12

Example 2

If AO = 5 and AD = 8, what is the length of DC?

One property of parallelograms, and therefore rectangles, is that the diagonals bisect each other. AC, then, has a measure that is twice the measure of AO.

rectangle ABCD with diagonals intersecting at point O, right triangle ADC is highlighted

AC = 2(5) = 10

Since the angles are all right angles, diagonal AC creates a right triangle.

82 + DC2 = 102

64 + DC2 = 100

DC2 = 36

DC = 6