Rectangle

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Rectangle is a type of quadrilateral (a polygon with four sides), which means it is a geometric shape with four sides and four angles. Key characteristic of a rectangle is that all of its angles are right angles, each measuring 90 degrees.

In a rectangle, there are two sets of sides:

• The longer sides are known as the length of the rectangle
• The shorter sides are referred to as the width of the rectangle

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These are the fundamental properties of a rectangle

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• Each angle in a rectangle measures exactly 90 degrees
• The sum of the angles in any quadrilateral, including a rectangle, is always 360 degrees
• Opposite sides of a rectangle are equal in length and parallel to each other. For example, as shown in the image below, in a rectangle ABCD, side AB || CD, and AD || BC.
• The diagonals of a rectangle (the line segments connecting opposite corners) are equal in length. In rectangle ABCD, as shown in the image below, AC = BD.
• The point, where the diagonals intersect, divides them into equal parts. In rectangle ABCD, the intersection point divides each diagonal into two equal segments, i.e. AO = OC = BO = OD 

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Interesting

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Is every quadrilateral with 90-degree angles a rectangle?

• • The answer is yes. If a quadrilateral has all angles measuring 90 degrees, it is defined as a rectangle

Can a rectangle be a square?

• • Indeed, a square is a special type of rectangle where all four sides have equal length, unlike a regular rectangle

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Examples

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Example 1

We have a rectangle named ABCD. If the length of its side AB is 14 cm, and the length of its side BC is 28 cm, what are the lengths of sides AD and CD?

Since ABCD is a rectangle, its opposite sides are equal in length. Therefore:

• side AD will also be 14 cm, and
• side CD will be 28 cm
• mirroring sides AB and BC, respectively

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Example 2

In this example we’re given a rectangle named ABCD. We know that the length of the diagonal BD is 26 cm. What is the length of the segment AO?

Since ABCD is a rectangle, a key property to remember is that the diagonals of a rectangle bisect each other. The point, where the diagonals intersect, point O, divides each diagonal into two equal segments.

In our specific example, diagonal BD is bisected at point O by another diagonal, therefore the lengths of BO, OD, AO, and OC are all equal:

• Since the total length of BD is 26 cm, and O divides BD into two equal parts, each segment (BO, OD, AO, and OC) will be half the length of BD
• BO = OD = AO = OC = BD : 2 = 26 cm : 2 = 13 cm

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