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Introduction To Euclid's Geometry

Question

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How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?

Solution

Two distinct intersecting lines cannot be parallel to the same line.

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

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