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.

In the given figure, lines EF and GH are parallel. Find the value of x if the lines AB and CD are also parallel.

If the angle - bisector of two intersecting chords of a circle passes through its centre , then prove that the chords are equal .

Two parallel straight lines are drawn through the points of intersection of two circles upto their circumference. Then prove that two straight lines are equal.

If a triangle is inscribed in an ellipse and two of its sides are parallel to the given straight lines, then prove that the third side touches the fixed ellipse.

Laxmi has drawn two circles which intersect each other at O externally. If PQ and RS be two parallel diameters of trhe circles, then prove that the points P, O and S are collinear.

Write the contrapositive and converse of the following statements. If the two lines are parallel, then they do not intersect in the same plane.

Prove that two adjacent angles of any parallel side of an isoceles trapezium are equal.

overset(harr)("AB ") and overset(harr)("DC ") are two parallel lines and a transversal l, intersects overset(harr)("AB ") at P and overset(harr)("DC ") at R. Prove that the bisectors of the interior angles form a rectangle.