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suppose that the following two definitions are agreed upon. a vertical line is a line containing the center of the earth. a horizontal line is a line perpendicular to some vertical line. (a) could two horizontal lines be parallel? (b) could two vertical lines be parallel? (c) could two vertical lines be perpendicular? (d) could two horizontal lines be perpendicular? (e) would every vertical line be a horizontal line? (0 would every horizontal line be a vertical line? (g) could a horizontal line be parallel to a vertical line? (h) would every line be horizontal?



Answer :

Two horizontal lines could not be parallel, two vertical lines could be perpendicular and horizontal line could be parallel to a vertical line. If they were, they would be parallel to each other and to the horizontal line perpendicular to both of them, which is possible.

a.)No; two horizontal lines could not be parallel. If two horizontal lines were parallel, then they would both be perpendicular to the same vertical line, which is impossible.

b.)No; two vertical lines could not be parallel.  If two vertical lines were parallel, then they would both contain the center of the earth, which is impossible.

c.)Yes; two vertical lines could be perpendicular. Therefore, if two vertical lines are perpendicular, then they are also perpendicular to each other.

d.)No; two horizontal lines could not be perpendicular. If two horizontal lines were perpendicular, then they would both be perpendicular to the same vertical line, which is impossible.

e.)Yes; every vertical line is a horizontal line. A vertical line is perpendicular to a horizontal line.

f.)No; not every horizontal line is a vertical line. A horizontal line is perpendicular to some vertical line.

g.)Yes; a horizontal line can be parallel to a vertical line.

h)No; not every line is horizontal.

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