CAT Introduction to Quadrilateral - Practice Questions & MCQ

You have studied that when we join two points, we get a line. And you also know about collinear and non-collinear points. Basically, if three or more points lying on the same line then the points are collinear . And, three or more points are not lying on the same line then the points are non-collinear.

If you join three non-collinear points in pairs, then the figure you obtained is a triangle.(Try and see if you get it or not).

Let's perform an activity

Mark four points in a paper and joining them in pairs in some order. You will observe that, if all the points are collinear (in the same line), you obtain a line segment, if three out of four points are collinear, you get a triangle and if no three points out of four are collinear, we obtain a closed figure with four sides.

So, a figure formed by joining four points in an order if no three points out of four are collinear is called a quadrilateral. A quadrilateral has four sides, four angles and four vertices.

quadri means four and lateral means side.

In quadrilateral ABCD, AB, BC, CD and DA are the four sides; A, B, C and D are the four vertices and ∠ A, ∠ B, ∠ C and ∠ D are the four angles formed at the vertices.

The line segments AC and BD, joining the opposite vertices are called the diagonals of quadrilateral. ABCD.

In this chapter, we will study more about different types of quadrilaterals, their properties, and especially those of parallelograms.

Angle Sum Property of a Quadrilateral

The angle sum property of a quadrilateral is one of the most important properties of a quadrilateral.

As you already know that the sum of the angles of a square or a rectangle is 360º. So is it possible that the sum of the angles of a quadrilateral is 360º?

This can be verified by drawing a diagonal and dividing the quadrilateral into two triangles.

Let ABCD be a quadrilateral and AC be a diagonal

Consider the ∆ ADC, as know that, the sum of the angles of a triangle is 180º.

                  ∠ DAC + ∠ ACD + ∠ D = 180°                           ...(1)   

Similarly, in ∆ ABC, 

                  ∠ CAB + ∠ ACB + ∠ B = 180°                           ...(2)

Adding (1) and (2), we get

          ∠ DAC + ∠ ACD + ∠ D + ∠ CAB + ∠ ACB + ∠ B = 180° + 180° = 360°

Also,  ∠ DAC + ∠ CAB = ∠ A and ∠ ACD + ∠ ACB = ∠ C

So,     ∠ A + ∠ D + ∠ B + ∠ C = 360°

i.e., the sum of the angles of a quadrilateral is 360°.