Using Euclid’s axioms/postulates bisect a given finite straight line.

Using Euclid’s axiom or postulate, prove the proposition that if in a triangle two angles are equal to one another, then the opposite sides are equal.

List five axioms (postulates) used in this book.

Does Euclid’sfifth postulate imply the existence of parallel lines ? Explain.

Why is axiom 5, in the list of Euclid’s axioms, considered as a ‘universal truth’ ?

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

Find the equations of the straight lines passing through the foot of the perpendicular from the point (2,3) upon the straight line 4x+3y+5=0 and bisecting the angles between the perpendicular and the given straight line.

If a graph is plotted between Iog k and 1/T the slope of the straight line so obtained is given by

Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.

Consider the following statement : There exists a pair of straight lines that are everywhere equidistant from one another. Do you think that this statement is (or is not) a direct consequence of Euclid’s fifth postulate ? Explain.

the line x+3y-2=0 bisects the angle between a pair of straight lines of which one has equation x-7y + 5 = 0 . The equation of the other line is :