explain how to justify the construction when the difference of two sides along with base angle is   given:
Case1 :  When AB> AC
Case 2 : When AB<AC.
REPLY IT AS SOON AS POSSIBLE.....ITS URGENT
 

Case 1:Let AB > AC that is AB – AC is given.

Steps of Construction:

1. Draw the base BC and at point B make an angle say XBC equal to the given angle.

2. Cut the line segment BD equal to AB – AC from ray BX.

3. Join DC and draw the perpendicular bisector, say PQ of DC.

4. Let it intersect BX at a point A. Join AC (see Fig. 11.6).

Then ABC is the required triangle.

Let us now see how you have obtained the required triangle ABC.

Base BC and ∠B are drawn as given. The point A lies on the perpendicular bisector of DC. Therefore,

AD = AC

So, BD = AB – AD = AB – AC.

Case 2:Let AB < AC that is AC – AB is given.

Steps of Construction:

1. Draw the base BC and at point B make an angle say XBC equal to the given angle.

2. Cut line segment BD equal to AC – AB from the line BX extended on opposite side of line segment BC.

3. Join DC and draw the perpendicular bisector, say PQ of DC.

4. Let PQ intersect BX at A. Join AC (see Fig. 11.7). Then, ABC is the required triangle.

You can justify the construction as in case (i).