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Constructions — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsConstructions4 Marks
Question
Using rulers and compasses only, construct a $\triangle\text{ABC}$ from the following data:
AB + BC + CA = 12cm, $\angle\text{B}=45^\circ$ and $\angle\text{C}=60^\circ$
✓

Answer


Steps of construction:
  1. Draw a line segment XY of 12cm.
  2. Draw $\angle\text{DXY}=45^\circ$ and $\angle\text{EYX}=60^\circ.$
  3. Draw the angle bisectors of $\angle\text{DXY}$ and $\angle\text{EYX}$ which intersect each other at A.
  4. Draw the perpendicular bisector of AX and AY which intersect XY at B and C respectively.
  5. Join AB and AC.
Hence $\triangle\text{ABC}$ is the required triangle.

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