(i) True — The shortest distance between two points is the straight line segment joining them.

(ii) True — A line extends indefinitely in both directions, so only a part of it can be shown on a sheet of paper.

(iii) True — Between any two points of a line segment, infinitely many points can be found.

(iv) False — Two parallel lines in a plane never intersect.

(v) False — Infinitely many lines can be drawn through a single given point.

(vi) False — Only one unique line can be drawn passing through two distinct points.

(vii) False — A simple closed curve is a polygon only if it is made up entirely of line segments. A circle, for example, is a simple closed curve but not a polygon.

(viii) True — The polygon with the least number of sides is a triangle, which has three sides.

(ix) False — A vertex of a quadrilateral lies on its boundary, not in its interior.

(x) False — A line segment with its end points on a circle is called a chord. It is called a diameter only when it also passes through the centre of the circle.

(xi) True — The diameter is the longest chord of the circle because it passes through the centre.

(xii) True — A diameter divides the circle into two equal arcs, each called a semicircle.

(xiii) True — A diameter divides the circular region into two equal parts, each called a semicircular region.

(xiv) True — All diameters of a circle pass through its centre, so they are concurrent at the centre.

(xv) True — A circle has a unique centre and the centre lies in the interior of the circle.

(xvi) False — A circle has infinitely many diameters (any chord passing through the centre is a diameter).