# Construction of a Triangle given its Base, Difference of the Other Two Sides and One Base Angle

**Given :** Base BC = x cm, AB - AC or AC â€“ AB = d cm and

**Required :**To construct a triangle ABC.

Case (i) AB > AC and AB - AC = d cm

Steps of construction:

1. Draw a ray BX and cut off a line segment BC = x cm.

2. Construct

3. Cut off a line segment BD = d cm on BY.

4. Join CD.

5. Draw a perpendicular bisector RS of CD intersecting BY at a point A.

6. Join AC.

ABC is the required triangle.

Case (ii) AB < AC and AC â€“ AB = d cmÂ

**Â Â Â**

Steps of construction

1. Draw a ray BX and cut off a line segment BC = x cm.

2. Construct a ray BY making an angle of Î¸ Â° with BC and produce YB to form a line YBYâ€™.

3. Cut off a line BDâ€™ = d cm on BYâ€™.

4. Join CDâ€™.

5. Draw perpendicular bisector RS of CDâ€™ intersecting BY at a point A.

6. Join AC.

ABC is the required triangle.Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â