Question

Construct a ΔABC in which BC = 4.5 cm, ∠C = 45° and sum of sides AB and AC is 8 cm. Justify your construction.

Answer 1

Given: In ΔABC, BC = 4.5 cm, ∠C = 45° and AB + AC = 8 cm

To construct: ΔABC

Steps of construction:

1. Draw a line segment BC = 4.5 cm.
2. At point C, make ∠XCB = 45°.
3. With C as centre, draw an arc of radius 8 cm to cut the ray CX at point D.
4. Join BD.
5. At point B, make ∠YBD = ∠BDC and let the ray BY intersect CD at point A.
Thus, ABC is the required triangle.


Justification:

In ΔABD,
As, ∠ABD = ∠BDC (By construction)
So, AB = AD (Sides opposite to equal angles are equal)

Now,
CD = 8 cm (By construction)
$\Rightarrow$AC + AD = 8 cm
So, AC + AB = 8 cm (Proved above)