Prove that the bisectors of a pair of vertically opposite angles are in the same straight line.

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.

If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.

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

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

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 __________.

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

From the top of a vertical tower, the angles of depression of two cars, in the same straight line with the base of the tower, at an instant are found to be 45° and 60°. If the cars are 100 m apart and are on the same side of the tower, find the height of the tower.

Prove that the internal bisectors of the angles of a triangle are concurrent

Prove that the bisectors of the interior angles of a rectangle form a square.