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

Solution:

We have to define ‘Ray’, ‘Straight line’ and a ‘point’.

Ray: A part of a line, which starts at a point (Here A) and goes off in a particular direction to infinity possibly through a second point (B in this case).

Straight Line: The basic concept about a line is that it should be straight, and it can be extended infinitely in both directions.

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 or height, it has only a position.

Perpendicular Distance: Shortest distance between a point and a line is known as perpendicular distance.

i) Parallel lines

• If the perpendicular distance between two lines is always constant, then these are called parallel.
• If the lengths of the common perpendiculars at different points on the lines are the same, then these lines are called parallel.
• In other words, the lines which never intersect each other are called parallel lines.

ii) Perpendicular lines: If the angle between two lines is equal to 90º, then these lines are perpendicular to each other.

CD ⊥ AB

AB ⊥ CD

iii) Line segment: A terminated line is called a line segment. It has two endpoints [A and B in this case.].

iv) Radius of a circle: The distance from the center to any point on the circle is called the radius of the circle.

v) Square: A square is a regular quadrilateral which means that it has four equal sides and four right angles.

 

☛ Check: NCERT Solutions for Class 9 Maths Chapter 5

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Video Solution:

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

NCERT Solutions Class 9 Maths Chapter 5 Exercise 5.1 Question 2

Summary:

We have to define ‘Ray’, ‘Straight line’ and a ‘point’.The lines that never intersect each other are called parallel lines, if the angle between two lines is equal to 90° then these lines are perpendicular to each other, a terminated line is called line segment and it has two endpoints, the distance from the center to any point on the circle is called the radius of the circle, and a square is a regular quadrilateral which means that it has four equal sides and four right angles.

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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 fig. 5.9, 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 = 1/2 AB. Explain by drawing the figure.