Prove that in a tetrahedron if two pairs of opposite edges are perpendicular , then the third pair is also perpendicular.

The two line of regression are perpendicular if

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

Prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square.

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 __________.

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.

prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square.

Prove that the lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent.

State which of the following statements are true (T) or which are false (F) If two lines in the same plane do not intersect, then they must be parallel. Distance between two parallel lines is not same everywhere. If m_|_l ,\ n\ _|_\ l and m\ !=n , then m n Two non-intersecting coplanar rays are parallel. No two parallel segments intersect. Every pair of lines is a pair of coplanar lines. Two lines perpendicular to the same line are parallel. A line perpendicular to one of two parallel lines is perpendicular to the other.

Two straight lines are cut by a transversal. If the bisectors of a pair of co-interior angles are perpendicular to each other , prove the two straight lines are parallel to each other.

A quadrilateral is a parallelogram, if its one pair of opposite sides are equal and parallel.