The quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic.

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

Two parallel lines l and m are intersected by a transversal p . Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.

ABCD is a cyclic quadrilateral (see Figure). Find the angles of the cyclic quadrilateral.

Theorem 10.11 : The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.

Complete each of the following, so as to make a true statement: A quadrilateral has ............ sides A quadrilateral has ............ angles. A quadrilateral has ............ vertices, no three of which are.... A quadrilateral has ............ diagonals. The number of pairs of adjacent angles of a quadrilateral is ...... The number of pairs of opposite angles of a quadrilateral is ...... The sum of the angles of quadrilateral is..... A diagonals of quadrilateral is a line segment that joins two ..... vertices of the quadrilateral. The sum of the angles of a quadrilateral is ......... right angles. The measure of each angle of a convex quadrilateral is ...... 180^0dot In a quadrilateral the point of intersection of the diagonals lie lies in .... of the quadrilateral. A point is in the interior of a convex quadrilateral, if it is in the ....... of its two opposite angles. A quadrilateral is convex if for each side, the remaining.... lie on the same side of the line containing the side.

Show that the quadrilateral, formed by joining the mid-points of the sides of a square is also a square.

Show that the quadrilateral, formed by joining the mid-points of the sides of a square, is also a square.

The sum of either pair of opposite angles of a cyclic quadrilateral is 180^0 OR The opposite angles of a cyclic quadrilateral are supplementary.

The sum of the angles in the four segments exterior to a cyclic quadrilateral is equal to 6 right angles.