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(i) Parallel lines

(ii) Perpendicular tines

(iii) Line segment

(iv) Radius of a circle

(v) Square

Answer :

i)Parallel lines: Two lines in a plane are said to be parallel, if they have no point in common.

In figure, x and y are said to be parallel because they have no point in common and we write, x||y .

Here, the term point is undefined.

ii)Perpendicular lines: Two lines in a plane are said to be perpendicular, if they intersect each other
at a right angle.

In figure, P and Q are said to be perpendicular lines because they intersect each other at \(90^\circ\).

iii)Line segment: The definite length between two points is called the line segment. ln figure, the
definite length between A and B is line segment and represented by AB.

iv)Radius of a circle: The distance from the centre to a point on the circle is called the radius of the
circle. ln the adjoining figure OA is the radius.

v)Square: A square can be defined as a rectangle having same length and breadth.

- 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 figures, 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 atleast 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 = \(\frac{1}{2} \) 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.
- In figure, if AC = BD, then prove that AB = CD.
- Why is axiom 5, in the list of Euclid’s axioms, considered a 'universal truth'? (Note that, the question is not about the fifth postulate.)

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