Construct a ∆ABC in which BC = 4.5 cm, ∠B = 45° and AB + AC = 8 cm. Justify your construction.

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Solution

Steps of construction:
1. Draw a line segment BC = 4.5 cm.
2. Construct $∠$ CBX = 45 $°$ .
3. Set off BP = 8 cm.
4. Join PC.
5. Draw the right bisector of PC, meeting BP at A.
6. Join AC.
Thus, $△$ ABC is the required triangle.

Justification:
In $△$ APC,
$∠$ ACP = $∠$ APC (By construction)
⇒ AC = AP (Sides opposite to equal angles are equal)
Now
AB = BP − AP = BP − AC
⇒ AB + AC = BP

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