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Introduction to Euclid's Geometry
Question
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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.

Answer

(i) False. This can be seen usually.
(ii)    False. This contradicts Axiom 5.1.
(iii)    True. Postulate 2.
(iv)    True. If we superimpose the region bounded by one circle on the other, then they coincide. So, their centres and boundaries coincide therefore, their radii will coincide.
(v) True. The first Axiom of Euclid.

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Some More Questions From Introduction to Euclid's Geometry Chapter

 Express the following statement as a linear equation in two variables by taking present ages (in years) of father and son as x and y, respectively. Age of father 5 years ago was two years more than 7 times the age of his son at that time.

Write the equation 2x = y in the form ax + by + c = 0 and find the values of a, b, c in the equation. How many solution this equation has?

Express the linear equation 7 = 2x in the form ax + by + c = 0 and also write the values of a, b and c

Write each of the following as an equation in two variables:

(i) x = – 5 (ii) y = 2

(iii) 2x = 3 (iv) 5y = 2.

 Which one of the following options is true, and why?

y = 3x + 5 has

(i) a unique solution,
(ii) only two solutions,
(iii) infinitely many solutions.