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 a triangle A B C , let P and Q be points on AB and AC respectively such that P Q || B C . Prove that the median A D bisects P Q .

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.

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 length of AB and AC.

The incircle of an isoceles triangle ABC, with AB=AC, touches the sides AB,BC and CA at D,E and F respecrively. Prove that E bisects BC.

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 equation of the line AC.

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.

A D is a median of Delta A B C . The bisector of /_A D B and /_A D C meet AB and AC in E and F respectively. Prove that EF||BC

In the following figure, F and E are points on the side AD of the triangle ABD. Through F a line is drawn parallel to AB to meet BD at point C . Prove that : ar (Delta ACE ) = ar (quad . BCEF )

The side AC of a triangle ABC is produced to point E so that CE=(1)/(2) AC. D is the mid-point of BC and ED produced meets AB at F. Lines through D and C are drawn parallel to AB which meet AC at point P and EF at point R respectively. Prove that: 3DF=EF

The bisectors of the angles B and C of a triangle A B C , meet the opposite sides in D and E respectively. If DE||BC , prove that the triangle is isosceles.