Construct a ∆ABC in which BC = 6 cm, ∠B = 30° and AB – AC = 3.5 cm. Justify your construction.

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Solution

Steps of construction:
1. Draw a line segment BC = 6 cm.
2. Construct $∠$ CBX = 30 $°$ .
3. Set off BD = 3.5 cm.
4. Join DC.
5. Draw the right bisector of DC, meeting BD produced at A.
6. Join AC.
Thus, $△$ ABC is the required triangle.

Justification:
Point A lies on the perpendicular bisector of DC.
⇒ AD = AC
Now
BD = AB − AD = AB − AC

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