Question

Construct an isosceles triangle in which: XY = XZ, YZ = 5.5 cm and ∠X = 60°

Answer 1

In ΔXYZ,
XY = XZ      ....(given)
c ∠XZY = ∠XYZ  ....(i)
∠X = 60°   ....(given)
Now, ∠X + ∠Y + ∠Z = 180°
60° + ∠Y + ∠Y = 180°     ....[From (i)]
2∠Y = 120°
⇒ ∠Y = 60° = ∠Z
Steps:
1. Draw YZ = 5.5cm.
2. Construct ∠YZP = 60° and ∠ZYQ = 60°
3. Ray ZP and YQ meet at x.
Thus, XYZ is the required triangle.