Question
Using rulers and compasses only, construct a $\triangle\text{ABC},$ given base $BC = 7\ cm$, $\angle\text{ABC}=60^\circ,$ and $AB + AC = 12\ cm$.
✓
Answer
Steps of Construction:
$1.$ Construct a line segment $BC$ of $7\ cm$.
$2.$ At the point $B$, draw $\angle\text{XBC}=60^\circ$
$3.$ Keeping $B$ as centre and radius $12\ cm$ draw an arc which intersects $XB$ at $D$.
$4.$ Join $DC$.
$5.$ Draw the perpendicular bisector of $DC$ which intersects $DB$ at $A$.
$6.$ Join $AC$.
Hence $\triangle\text{ABC}$ is the required triangle.
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