Construct $\Delta ABC$ in which $BC = 7 \, cm$,$\angle B = 45^{\circ}$ and $AC - AB = 2 \, cm$. Write the steps of construction.
(N/A) Steps of construction:
$1$. Draw a line segment $BC = 7 \, cm$.
$2$. At point $B$,construct an angle $\angle XBC = 45^{\circ}$.
$3$. Cut a line segment $BD = 2 \, cm$ from the ray $BX$ (since $AC - AB > 0$,$D$ is on the ray $BX$).
$4$. Join $DC$.
$5$. Draw the perpendicular bisector of $DC$,let it intersect $BX$ at point $A$.
$6$. Join $AC$. Thus,$\Delta ABC$ is the required triangle.
$1$. Draw a line segment $BC = 7 \, cm$.
$2$. At point $B$,construct an angle $\angle XBC = 45^{\circ}$.
$3$. Cut a line segment $BD = 2 \, cm$ from the ray $BX$ (since $AC - AB > 0$,$D$ is on the ray $BX$).
$4$. Join $DC$.
$5$. Draw the perpendicular bisector of $DC$,let it intersect $BX$ at point $A$.
$6$. Join $AC$. Thus,$\Delta ABC$ is the required triangle.
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