Two parallel lines l and m are intersected by a transversal p (see the given figure). Show that the quadrilateral formed by the bisector of interior angles is a rectangle.

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.

ABCD is a cyclic quadrilateral (see the given figure). Find the angles of the cyclic quadrilateral.

Show that the bisectors of angles of a parallelogram form a rectangle.

ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that angle ABD = angle ACD .

AB and CD are respec­tively the smallest and longest sides of a quadrilateral ABCD (see th e given figure). Show that angle A gt angle C and angle B gt angle D

AD and BC are equal perpendiculars to a line segment AB (see the given figure) Show that CD bisects AB.

P is a point equidistant from two lines l and m intersecting at point A (see figure). Show that the line AP bisects the angle between them.

If a transversal intersects two parallel lines, then prove that each pair of alternate interior angles is equal.

l and m are two parallel lines intersected by another pair of parallel lines p and q . Show that DeltaABC~= DeltaCDA .

l, m and n are three parallel lines intersected by transversals р and q such that l , m and n cut off equal intercepts AB and BC on p (see the given figure). Show that l, m and n cut off equal intercepts DE and EF on q also.