If a point C lies between two points A and B, such that `AC=BC`, then prove that `AC=1/2 AB`. Explain by drawing the figure.

In the figure, If AC=BD then prove that AB=CD.

If A,B,C are three points on a line and B lies between A and C, then prove that AC-AB = BC

D is a point on side BC ΔABC such that AD = AC (see figure). Show that AB > AD.

In Delta ABC , /_ B = /_C , D and E are the points on AB and AC such that BD = CE , prove that DE || BC .

Let ABC be a triangle and D and E be two points on sides AB such that AD = BE . If DP || BC and EQ || AC , then prove that PQ || AB .

In a Delta ABC , let P and Q be points on AB and AC respectively such that PQ || BC . Prove that the median AD bisects PQ.

In Fig .D is a point on side BC of DeltaABC such that (BD)/(CD) =(AB)/(AC) prove that AD is the bisector of angleBAC.

If D, E and F are respectively, the mid-points of AB, AC and BC in DeltaABC , then BE + AF is equal to

If A, B, C and D aare four points and vec AB = vec DC then vec AC + vec BD =

Draw a ray AB with initial point A and construct a ray AC such that angleBAC = 60°.