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Introduction to Euclid's Geometry
Question
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Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

Answer

If a straight line l falls on two straight lines m and n such that sum of the interior angles on one side of l is two right angles, then by Euclid’s fifth postulate the lines m and n will not meet on this side of I. Next, we know that the sum of the interior angles on the other side of line l will also be two right angles.

Therefore, they will not meet on the other side also. So, the lines m and n never meet and are, therefore parallel.

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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.

Write four solutions for each of the following equations:

2x + y = 7