Question

Construct an isosceles triangle in which: Base DE = 6 cm and ∠F = 45°

Answer 1

In isosceles ΔDEF,
Base DE = 6cm
∠F = 45°        ....(given)
⇒ ∠D = ∠E   ....(DEF is isosceles triangle)
Now, ∠D + ∠E + ∠F = 180°
2∠D + 45 = 180°
2∠D = 135°
⇒ ∠D = ∠E = 67.5°
Steps:
1. Draw DE = 6cm.
2. Construct ∠DEP = 67.5° and ∠EDQ = 67.5°
3. Ray EP and ray DQ meets at F.
Thus, DEF is the required triangle.