State whether the following statement is True or False. Justify your answer.
"For every line $l$ and for every point $P$ not lying on a given line $l$,there exists a unique line $m$ passing through $P$ and parallel to $l$." This is known as Playfair's axiom.

Study the following statement: "Two intersecting lines cannot be perpendicular to the same line". Check whether it is an equivalent version to Euclid's fifth postulate.

Does Euclid's fifth postulate imply the existence of parallel lines? Explain.

The total number of propositions in the Elements are:

Write whether the following statement is True or False. Justify your answer.
In the Vedic period,square and circular-shaped altars were used for household rituals,while altars whose shapes were combinations of rectangles,triangles,and trapeziums were used for public worship.

Give a definition for perpendicular lines. Are there other terms that need to be defined first? What are they,and how might you define them?