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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 – AB = d cm and

ABC = θ° of a triangle.
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

YBC = θ°.
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 – AB = d cm    

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 θ ° with BC and produce YB to form a line YBY’.
3. Cut off a line BD’ = d cm on BY’.
4. Join CD’.
5. Draw perpendicular bisector RS of CD’ intersecting BY at a point A.
6. Join AC.
ABC is the required triangle. 
                                                         





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