Question

$Constructa\Delta ABCinwhichBC=4.5cm,\angle B={45}^{\circ }andAB+AC=8cm\text{Justify your constructions.}$

Answer 1

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,
$\angle ACP$ = $\angle APC$ (By construction)
⇒ AC = AP (Sides opposite to equal angles are equal)
Now
AB = BP − AP = BP − AC
⇒ AB + AC = BP