What is a Quadrilateral?
We know that a polygon is a closed two-dimensional shape with three or more sides. A quadrilateral is a type of polygon.
Side– A side is a straight line or straight boundary of two dimensional polygons.
Vertex: A vertex is a point where two lines of a polygon meet or intersect.
Angle: Where two sides of a quadrilateral meet, an angle is formed. It is formed when two different sides have a common point. It shows the measure of orientation of one line with respect to the other.
The word quadrilateral is formed from two latin words, ‘quadri’ and ‘latus’. The word ‘Quadri’ means four and ‘Latus’ means side. So, a quadrilateral is a polygon of four sides, four vertices and four angles. In our daily life we come across a number of objects that are shaped like quadrilaterals, for example, kites, dollar bills, chess boards, tables etc. The different geometrical shapes of quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids, and kites.
Parallel Sides and Right Angles in a Quadrilateral
Parallel sides: Parallel sides are the two sides that are always the same distance apart in any figure. There may be one or two pairs of parallel sides in a quadrilateral.
Right angle: A Right angle is a ‘L’ shaped angle. Its measure is 90 degrees. It is also marked as ‘L’ in the figures as shown,
Let’s find the pair of parallel lines and the right angle of this given polygon.
The two pairs of blue and green lines are parallel lines. So, there are two pairs of parallel lines. And, the two angles marked ‘L’ are right angles. Hence, there are two right angles.
Types of Quadrilaterals
Quadrilaterals are specially named on the basis of their number of sides and angles respectively. There are several types of quadrilaterals, such as,
Trapezoid:
A trapezoid is a quadrilateral that has exactly one pair of parallel sides. In the given quadrilateral the two green lines are parallel sides. Therefore, it is a trapezoid.
Parallelogram:
A parallelogram is a quadrilateral that has two pairs of parallel sides. In the figure two green and two red lines are two pairs of parallel sides. So, it is a parallelogram. The opposite sides of a parallelogram, which are parallel, are also equal in length.
Rectangle:
A rectangle has two pairs of parallel sides and four right angles. The opposite sides of a rectangle are also equal in length.
Rhombus:
A Rhombus has two pairs of parallel sides and all the four sides are equal in length. The two pairs of red and green lines form parallel pairs of lines.
Square:
A square has two pairs of parallel sides, four equal sides and four right angles.
Kite:
A kite has two pairs of adjacent sides that are equal in length. Where the two non-equal sides meet, the angles formed are equal to each other.
How to Draw a Quadrilateral?
Drawing quadrilaterals is very simple. We can draw the quadrilaterals using the four vertices and the four corresponding sides. We can also model each on our geoboard. Move one vertex of any random quadrilateral according to the conditions and make new quadrilaterals.
Drawing a Quadrilateral that has Four Right Angles
There are two types of quadrilaterals which satisfy this condition. The rectangle and square both have four interior right angles. So, we can draw both figures as,
Step 1: Draw 1 side on the board.
Step 2: Draw a perpendicular line on one vertex.
Step 3: Draw a perpendicular line on the second vertex.
Step 4: Join two vertices obtained.
Solved Examples
Example 1: There is a ‘STOP’ signal on a wall. Can you count the right angles and pair of parallel lines on the signal post.
Solution:
There are 4 pairs of parallel sides, a pair of yellow lines, a pair of blue lines, a pair of green lines and a pair of purple lines. And, there isn’t any right angle in the given figure.
So,
Number of Right angles: 0
Pair of parallel sides: 4
Example 2: Identify the number of right angles and pair of parallel sides in each of the following quadrilaterals.
Solution:
Number of Right angles: 1
Pair of parallel sides: 1
Number of Right angles: 4
Pair of parallel sides: 2
Number of Right angles: 0
Pair of parallel sides: 2
Number of Right angles: 1
Pair of parallel sides: 0
Example 3: Identify the figures.
Solution:
Pair of parallel sides: 2
Number of Right angles: 0
Equal sides: 4
So, the given figure is a Rhombus.
Example 4: How are the parallelograms and rhombuses alike? How are they different?
Solution:
Parallelograms & rhombuses are same in following ways:
Each has four sides
Each has four angles.
Each has two pairs of parallel sides.
Parallelograms & rhombuses are different in following way:
Rhombus always has 4 equal sides. However, this is not necessarily true for a parallelogram.
Example 5: How are parallelograms and squares alike? How are they different?
Solution:
Parallelograms & squares are same in following ways :
Each has four sides.
Each has four angles.
Each has two pairs of parallel sides.
Parallelograms & squares are different in following ways:
Squares always have 4 equal sides and 4 right angles. However, this is not necessarily true for a parallelogram.
Less than three sides can not enclose any area. Polygon is a closed figure. So, at least 3 sides are required to make a polygon.
If all the angles of a parallelogram are right angles, then we get a Rectangle.
If four sides of a quadrilateral are equal, then the quadrilateral is said to be a Rhombus. Square also has 4 equal sides.
There are exactly 4 sides in a quadrilateral.
There are exactly 4 angles in a quadrilateral.