In Geometry we learn about different shapes which may be one-dimensional, 2-dimentional or 3-dimentional. The Basic Terms we must know in geometry are line segments. A Line Segment is formed by joining two points on a plane. It has only length & is thus 1-dimentional. But more than 2 points on a plane may or may not lie in the same line. If they lie in the same line, they are called Collinear Points. But, if they do not lie in the same line, they are called non-collinear points.
Collinear points lie in the same line, so any number of collinear points will always give only a single line. But non-collinear points joined together form some closed & some open figures, of which closed figures are called polygons. Thus, a Polygon is a closed figure formed by drawing three or more line segments. These line segments are the sides of the polygon. Thus, a polygon has at least 3 sides. Depending upon the number of sides of polygons, they are given different names.
A polygon formed with 3 non-collinear points has 3 sides & is called a triangle, while one drawn with 4 non-collinear points is called a quadrilateral; 5-sided polygon is a pentagon & so on.
On the basis of the properties of sides & angles, quadrilaterals are also put in different categories as square, rectangle, parallelogram, etc.
Let’s try to know about squares. A square is a close polygon which shows the following properties:
1. It is a quadrilateral, i.e., it has four sides, 4 angles & 4 vertices.
2. All 4 sides are of equal length.
3. All angles of a square are right angles, i.e., 90 ̊ each.
4. Sum of all the angles of a square is 360 ̊.
In brief, a square is a quadrilateral in which all the four sides are equal & each angle measures 90 ̊.
We know that difference between two Numbers is obtained by subtracting one number from another. This subtraction is shown by the ‘-’ symbol. If A and B are two numbers then A – B is known as difference. Sum of the two numbers A and B is given by the addition of two numbers. Symbol ‘+’ is used to show the addition. Mathematically it is represented as A + B. Term Square refers to two times multiplication of the given number by itself. That is the square of the number A is A * A. It is also represented as (A) 2.
Product of two numbers is given by simply multiplying two numbers that is if A and B are two numbers then their product will be (A * B).
If the difference between two no is 9 and the product of the two is 14, what is the square of their sum?
Solution: Let’s take two numbers - 7 and 2. Difference of these two numbers is 9. Mathematically, it can be shown as, if A = 7 and B = 2 then difference will be 7 – (- 2) = 9 and their product will be 14 that is
(7 * (- 2)) = - 14,
Now sum of these two numbers will be given by following formula:
A + B = 7 + (-2) = 7 – 2 = 5,
Square of sum of given number will be given as:
[7 + (-2)] 2 = (7 – 2) 2 = (5) 2 = 5 * 5 = 25. Thus final answer will be 25 (square of sum of given numbers) for those numbers whose difference is equals to 9 and whose product is equals to – 14.