In this article, we’re going to understand about special kinds of polygons called Quadrilaterals. Television screen, an envelope or a canvas are all examples of quadrilaterals. Quadrilateral is one word but you would like to know that “quadri” basically means “four” and lateral means “sides”. If you realise, all the above mentioned objects have four sides. To name a quadrilateral, we should assign names to four points ABCD.
These things that we just named are called vertices. Keep in mind that a quadrilateral will always have four vertices. Each point is called a vertex and as we’ve already read that a quadrilateral has four sides and the sides are AB, BC, CD, DA. Now you must remember that every quadrilateral has four sides and four vertices. Now let’s move onto another important property of quadrilaterals. Consider a table. You know how the surface of the table is flat, it’s a plain surface. Now if you were to draw a quadrilateral in there, you will see how all the vertices and sides of the quadrilateral lie on one plane. So we can now say that a quadrilateral has four sides, four vertices and is a closed figure lying on one plane. You would also like to know that a vertex is formed when two sides meet at a point. What is formed between those sides is called an angle. A quadrilateral is also defined by its angles. It has four angles.
Marked above are the angles as well. How do we name the angles? How do we name the green angle? Well, we can call it angle C. You just name the angle based on the vertex at which it is formed. But a better way to name it would be to call it DCB or BCD. In this case, we named it based on the sides. The last basic concept you need to know is that vertices A and C are opposite to each other, and vertices B and D are opposite to each other. The lines joining the opposite vertices are called diagonals. In the above figure, we can say that AC and BD are the diagonals. Now let’s take a look into the different type of quadrilaterals:
Square: All sides are of equal lengths.
BC = CD = DA = AB.
All the angles are right angles. Angle B = Angle A = Angle C = Angle D = 90 degrees. It’s opposite sides are parallel. AB is parallel to CD and BC is parallel to AD.
In rectangle ABCD, opposite sides are of equal lengths that is AB is equal to DC and AD is equal to BC. All the angles are right angles which means that Angle A = angle B = angle D = angle C = 90 degrees. It’s opposite sides are parallel, AB || BC || CD || DA.
Opposite sides are of equal lengths. DV = AB and DA = CB. Opposite angles are of equal measures, that is Angle D is equal to angle B and angle A is equal to angle C. Opposite sides are parallel, that is DC is equal to AB and DA is equal to CB.
Only one pair of the opposite sides are parallel which is AB is || to DC. The other two non parallel sides are called slant sides. Here the slant sides are AD and BC. When the measures of slant sides are the same, it is called an isosceles trapezium. An isosceles trapezium has two pairs of similar angles. Here, angle A and angle B, Angle D and angle C are the two pairs of similar angles.
All sides are of equal lengths which is AD = DC =CB = BA. Opposite angles are of equal measures. Angles A and Angle C are the same and Angle D and angle B are the same. Opposite sides are parallel that is AC is parallel to BC, and AB is parallel to DC.
In kite ABCD, two distinct pairs of adjacent sides are of equal lengths that is CB is equal to CB and DA is equal to AB. One Pair of opposite angles is of equal measure that is Angle B is equal to angle D.
So here we have quadrilaterals and its type. If you wish to study and learn more about the same, then check out doubtnut.com to grasp knowledge about various concepts through video based explanations and doubt clearance.