Question 48

State whether the statements are true(T) or false(F).

With ruler and compasses, we can bisect any given line segment.

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Solution

True
A perpendicular bisector is a line segment which is perpendicular to the given line and divides the given line segment into two equal halves.
With ruler and compass, we can draw a perpendicular bisector for any line segment.

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Question 49

State whether the statements are true (T) or false (F).

Only one perpendicular bisector can be drawn to a given line segment.

Draw any line segment $¯ ¯¯¯¯¯¯ ¯ A B$ . Mark any point $M$ on it. Through $M,$ draw a perpendicular to $¯ ¯¯¯¯¯¯ ¯ A B$ . (Use ruler and compasses)

A

A \subseteq ϕ \Leftrightarrow A = ϕ

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