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Question

Complete each of the following, so as to make a true statement:
(i) A quadrilateral has ______sides.
(ii) A quadrilateral has ______angles.
(iii) A quadrilateral has ______vertices, no three of which are ______
(iv) A quadrilateral has ______diagonals.
(v) The number of pairs of adjacent angles of a quadrilateral is ______
(vi) The number of pairs of opposite angles of a quadrilateral is ______
(vii) The sum of the angles of a quadilateral is ______
(viii) A diagonal of a quadrilateral is a line segment that joins two ______vertices of the quadrilateral.
(ix) The sum of the angles of a quadrilateral is ______ right angles. (x) The measure of each angle of a convex quadrilateral is ______ 180.
(xi) In a quadrilateral the point of intersection of the diagonals lies in ______ of the quadrilateral.
(xii) A point is in the interior of a convex quadrilateral, if it is in the ______ of its two opposite angles.
(xiii) A quadrilateral is convex if for each side, the remaining ______ lie on the same side of the line containing the side.

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Solution

(i) A quadrilateral has four sides.
(ii) A quadrilateral has four angles.
(iii) A quadrilateral has four vertices, no three of which are collinear.
(iv) A quadrilateral has two diagonals.
(v) The number of pairs of adjacent angles of a quadrilateral is four.
(vi) The number of pairs of opposite angles of a quadrilateral is two.
(vii) The sum of the angles of a quadilateral is 360.
(viii) A diagonal of a quadrilateral is a line segment that joins two opposite vertices of the quadrilateral.
(ix) The sum of the angles of a quadrilateral is 4 right angles.
(x) The measure of each angle of a convex quadrilateral is less than 180.
(xi) In a quadrilateral the point of intersection of the diagonals lies in interior of the quadrilateral.
(xii) A point is in the interior of a convex quadrilateral, if it is in the interior of its two opposite angles.
(xiii) A quadrilateral is convex if for each side, the remaining vertices lie on the same side of the line containing the side.


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