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

Find the measure of each angle indicated in each figure where l and m are parallel lines intersected by transversal n.

AD is a median of triangleABC . A straight line parallel to BC intersect AB and AC at P and Q respectively. Prove that AD bisects PQ.

Two circles intersect each other at the points P and Q. Two straight lines through P and Q intersect on circle at the points A and C and the other circle at B and D . Prove that AC||BD.

In triangleABC , a straight line parallel to BC intersects the sides AB and AC at P and Q respectively. If AP = 8cm, CQ = 9cm and AQ = 2BP, then BP=

P_1 and P_2 are planes passing through origin L_1 and L_2 are two lines on P_1 and P_2, respectively, such that their intersection is the origin. Show that there exist points A ,B and C , whose permutation A^(prime),B^(prime)a n dC^(prime), respectively, can be chosen such that i) A is on L_1,B on P_1 but not on L_1 and C not on P_1; ii) A ' is on L_2,B ' on P_2 but not on L_2 and C ' not on P_2dot

Two circle intersect each other at A and B and a straight line parallel to AB intersects the circles at C,D,E,F. Prove that CD = EF.

Line L has intercepts a and b on the coordinate axes. When the axes are rotated through given angle, keeping the origin fixed, the same line L has intercepts p and q, then

If three equal positive numbes a,b,c are in G.P,then show that a+c>2b