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 give figure, the arms of two angles 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.

Fill in the blanks: If two lines intersect at a point, and if one pair of vertically opposite angels are acute angles, then the other pair of vertically opposite angles are ______.

The equation of the pair of lines through the points (a, b) parallel to the coordinate axes is

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

Given the linear equation 3x+2y-8=0 , write another linear equation in two variables such that the geometric representation of the pair so formed is: (i) Intersecting lines (ii) Parallel lines (iii) Coincident lines

If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

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.