Question

Answer the following questions
(i) How many pairs of adjacent sides does a quadrilateral have?
(ii) How many pairs of opposite sides does a quadrilateral have?
(iii) How many pairs of adjacent angles does a quadrilateral have?
(iv) How many pairs of opposite angles does a quadrilateral have?
(v) How many diagonals does a quadrilateral have?

Answer 1

Hint:In this question, first of all, draw a quadrilateral ABCD. Now mark each side and angle of it. Now, also mark the parameter asked in various questions and count the number of them.

Complete step-by-step answer:
Before proceeding with this question, we must know what a quadrilateral is. A quadrilateral is a polygon with four edges and four-vectors of four corners. A quadrilateral can be any polygon having four sides regular or irregular. Some regular quadrilateral are square, rectangle, rhombus, etc. Below is the figure of an irregular quadrilateral.

Now, let us consider our questions.
(i) Here, we have to find the pairs of the adjacent sides of a quadrilateral.
Let us consider a quadrilateral ABCD,

In the above figure, sides AB and BC, BC and DC, DC and DA, and DA and AB are adjacent to each other. So, we get the total number of pairs of adjacent sides in the quadrilateral as four.
(ii) Here, we have to find the pairs of opposite sides of a quadrilateral.
Let us consider a quadrilateral ABCD,

In the above figure, sides AB and DC and BC and AD are opposite to each other. So, we get the number of pairs of opposite sides in quadrilateral as 2.
(iii) Here, we have to find the pairs of the adjacent angles of a quadrilateral.
Let us consider a quadrilateral ABCD,

In the above figure, angles A and B, angles B and C, angles C and D, and angles D and A are adjacent to each other. So, we get the number of pairs of adjacent angels as 4.
(iv) Here, we have to find the pairs of the opposite angles a quadrilateral has.
Let us consider a quadrilateral ABCD,

In the above figure, we can see that the angles A and C and angles B and D are opposite to each other. So, we get the number of pairs of opposite angles as 2.
(v) Here, we have to find the number of diagonals that a quadrilateral has.
Let us consider a quadrilateral ABCD,

In the above figure, we can see that the diagonals are AC and BC. So, we get the number of diagonals as 2.

Note: In this question, students must properly count every part of the quadrilateral in which some are 4 and some are 2. Also, students must note that the above results are true for every kind of quadrilateral. Students are advised to draw the figure in the questions of geometry to visualize the question.