Mathematics
Give a definition for each of the following terms. Are there other terms that need to be defined first? What are they, and how might you define them?
(i) parallel lines
(ii) perpendicular lines
(iii) line segment
(iv) radius of a circle
(v) square
Euclid's Geometry
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Answer
We have to define some other terms like : Ray, Straight line and a Point.
Ray - A ray is a part of a line, that has a fixed starting point but no end point. It can extend infinitely in one direction.
Straight Line - A line that connects two points in a plane and extends to infinity in both directions. It is considered one dimensional figure.
Point - A small dot made by a sharp pencil on a sheet of paper gives an idea about a point. A point has no dimension i.e, length, breadth and height, it has only a position.
(i) If the perpendicular distance between two lines is constant, then these lines are considered parallel to each other.
(ii) If the angle between two lines is equal to 90°, then these lines are considered perpendicular to each other.
(iii) A part of a line that has two endpoints and is the shortest distance between them, is a line segment.
(iv) The distance from the center to any point on the circumference of the circle is called the radius of the circle.
(v) A square is a regular quadrilateral that has four equal sides and angle between each side is a right angle.
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Related Questions
Which of the following statements are true and which are false? Give reasons for your answers.
(i) Only one line can pass through a single point.
(ii) There are an infinite number of lines which pass through two distinct points.
(iii) A terminated line can be produced indefinitely on both the sides.
(iv) If two circles are equal, then their radii are equal.
(v) In figure, if AB = PQ and PQ = XY, then AB = XY.
Consider two ‘postulates’ given below:
(i) Given any two distinct points A and B, there exists a third point C which is in between A and B.
(ii) There exist at least three points that are not on the same line.
Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid’s postulates? Explain.
If a point C lies between two points A and B such that AC = BC, then prove that AC = AB. Explain by drawing the figure.
In Question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.