Construct $\Delta ABC$ with $AB = 6 \text{ cm}$,$BC = 7 \text{ cm}$,and $AC = 5 \text{ cm}$. Then,construct $\Delta BXY$ similar to $\Delta ABC$ such that its sides are $\frac{4}{5}$ of the corresponding sides of $\Delta ABC$. Write the steps of construction.
(N/A) Steps of construction:
$1$. Draw a line segment $BC = 7 \text{ cm}$.
$2$. With $B$ as the center and radius $6 \text{ cm}$,draw an arc. With $C$ as the center and radius $5 \text{ cm}$,draw another arc intersecting the first arc at $A$.
$3$. Join $AB$ and $AC$ to form $\Delta ABC$.
$4$. Draw a ray $BX$ making an acute angle with $BC$ on the side opposite to vertex $A$.
$5$. Locate $5$ points $B_1, B_2, B_3, B_4, B_5$ on $BX$ such that $BB_1 = B_1B_2 = B_2B_3 = B_3B_4 = B_4B_5$.
$6$. Join $B_5C$.
$7$. From $B_4$,draw $B_4Y \parallel B_5C$ meeting $BC$ at $Y$.
$8$. From $Y$,draw $YX \parallel CA$ meeting $AB$ at $X$. Then $\Delta BXY$ is the required triangle.
$1$. Draw a line segment $BC = 7 \text{ cm}$.
$2$. With $B$ as the center and radius $6 \text{ cm}$,draw an arc. With $C$ as the center and radius $5 \text{ cm}$,draw another arc intersecting the first arc at $A$.
$3$. Join $AB$ and $AC$ to form $\Delta ABC$.
$4$. Draw a ray $BX$ making an acute angle with $BC$ on the side opposite to vertex $A$.
$5$. Locate $5$ points $B_1, B_2, B_3, B_4, B_5$ on $BX$ such that $BB_1 = B_1B_2 = B_2B_3 = B_3B_4 = B_4B_5$.
$6$. Join $B_5C$.
$7$. From $B_4$,draw $B_4Y \parallel B_5C$ meeting $BC$ at $Y$.
$8$. From $Y$,draw $YX \parallel CA$ meeting $AB$ at $X$. Then $\Delta BXY$ is the required triangle.
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