If two straight lines intersect each other, prove that the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.

If two lines intersect prove that the vertically opposite angles are equal

Show that the bisector of vertical angle of an isosceles triangle bisects the base at right angles.

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.

Fill in the blanks:(i) If two angles are complementary, then the sum of their measures is _______.(ii) If two angles are supplementary, then the sum of their measures is ______.(iii) Two angles forming a linear pair are _______________.(iv) If two adjacent angles are supplementary, they form a ___________.(v) If two lines intersect at a point, then the vertically opposite angles are always_____________.(vi) If two lines intersect at a point, and if one pair of vertically opposite angles areacute angles, then the other pair of vertically opposite angles are __________.

If two parallel lines intersected by a transversal; prove that the bisectors of the two pairs of interior angle encloses a rectangle.

If two parallel lines are intersected by a transversal, prove that the bisectors of the interior angles on the same side of transversal intersect each other at right angles.

Prove that the bisectors of opposite angles of a parallelogram are parallel.

A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

In a parallelogram, prove that the bisectors of any two consecutive angles intersect at right angle.