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

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

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.

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 __________.

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.

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.

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.

A point O inside a rectangle A B C D is joined to the vertices. Prove that the sum of the areas of a pair of opposite triangles so formed is equal to the sum of the areas of other pair of triangles.

One angle of a triangle is equal to one angle of another triangle and the bisectors of these two equal angles divide the opposite sides in the same ratio, prove that the triangles are similar.