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