M and N divide the side AB of a triangle ABC into three equal parts . Through M and N, lines are drawn parallel to BC and intersecting AC at points P and Q respectively. Prove that P and Q divide AC into three equal parts.

ABC is a triangle A line is drawn parallel to BC to meet AB and AC in D and E respectively. Prove that the median through A bisects DE.

In triangle ABC, D and E are points on side AB such that AD = DE = EB. Through D and E, lines are drawn parallel to BC which meet side AC at points F and G respectively. Through F and Glines are drawn parallel to AB which meet side BC at points M and N respectively. Prove that : BM = MN = NC.

P Q R is a triangle in which P Q=P R and S is any point on the side P Q . Through S , a line is drawn parallel to Q R and intersecting P R at Tdot Prove that P S=P Tdot

P Q R is a triangle is which P Q=P R\ a n d\ S is any point on the side P Q . Through S , a line is drawn parallel to Q R and intersecting P R\ at Tdot Prove that P S=P T

BC is an equilateral triangle. A circle is drawn with centre A so that it cuts AB and AC at points M and N respectively. Prove that BN = CM

In the figure, given, ABC is a triangle and BC is parallel to the y-axis. AB and AC intersect the y-axis at P and Q respectively. Find the ratio in which divides AC.

In the given figure ABC is a triangle and BC is parallel to the Y-axis. AB and AC intersects the y-axis at Pand Q respectively. (iii) Find the ratio in which Q divides AC.

The diagonals of a parallelogram A B C D intersect at a point O . Through O , a line is drawn to intersect A D\ at P and B C at Q . Show that P Q divides the parallelogram into two parts of equal area.

The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line a drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.

D and F are the mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Find AB, if EF=4.8cm .