Question

Construct $∆$DEF such that EF = 4.8 cm, $\angle$E = 50$°$ and DE + DF = 8.3 cm.

Answer 1

Steps of construction:
1. Draw EF = 4.8 cm.
2. Draw ray EX, such that $\angle \mathrm{FEX}=50°$.
3. With E as centre and radius 8.3 cm, draw an arc, intersecting ray EX at point P.
4. Join P and F.
5. Draw the perpendicular bisector of seg PF, intersecting seg EP at point D.
6. Join D and F.
7. Hence, $△$DEF is the required triangle.