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Constructions — Maths STD 9 — Question

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

Answer


Steps of construction:
$1.$ Draw a line segment $XY$ of $12\ cm$.
$2.$ 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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