l, m and n are three parallel lines intersected by the transversals p and q at A, B, C and D,E, F such that they make equal intercepts AB and BC on the transversal p. Show that the intercepts DE and EF on q are also equal.

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.

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

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.

If a, b, c be the pth, qth and rth terms respectively of a HP, show that the points (bc, p), (ca, q) and (ab, r) are collinear.

AB is a line segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (see the given figure). Show that the line PQ is the perpendicular bisector of AB.

AB is a line - segment. P and Q are points on either side of AB such that each of them is equidistant from the points A and B (See Fig ). Show that the line PQ is the perpendicular bisector of AB.

Points P, Q, R and S divide the line segment joining the points A(1,2) and B(6,7) in 5 equal parts. Find the coordinates of P,Q and R.

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.

ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that the perimeter of DeltaPQR is double the perimeter of DeltaABC.

Equal charges q are placed at the three corners B, C, D of a square ABCD of side a. The potential at A is