Draw $\Delta PQR$ with $QR = 7 \, cm$,$m\angle Q = 45^{\circ}$ and $m\angle R = 60^{\circ}$. Then construct $\Delta QAB$ similar to $\Delta PQR$ whose sides have lengths $\frac{4}{3}$ times the lengths of corresponding sides of $\Delta PQR$. Write the steps of construction.
(N/A) Steps of construction:
$1$. Draw a line segment $QR = 7 \, cm$.
$2$. At point $Q$,construct an angle of $45^{\circ}$ using a protractor or compass.
$3$. At point $R$,construct an angle of $60^{\circ}$ using a compass.
$4$. Let the intersection of these two rays be point $P$. Thus,$\Delta PQR$ is formed.
$5$. Draw an acute angle $\angle RQX$ below the base $QR$.
$6$. Locate $4$ points $Q_1, Q_2, Q_3, Q_4$ on ray $QX$ such that $QQ_1 = Q_1Q_2 = Q_2Q_3 = Q_3Q_4$.
$7$. Join $Q_3$ to $R$. Draw a line through $Q_4$ parallel to $Q_3R$ intersecting the extended line segment $QR$ at $R'$.
$8$. Draw a line through $R'$ parallel to $RP$ intersecting the extended line segment $QP$ at $P'$.
$9$. $\Delta P'QR'$ is the required triangle similar to $\Delta PQR$ with a scale factor of $\frac{4}{3}$.
$1$. Draw a line segment $QR = 7 \, cm$.
$2$. At point $Q$,construct an angle of $45^{\circ}$ using a protractor or compass.
$3$. At point $R$,construct an angle of $60^{\circ}$ using a compass.
$4$. Let the intersection of these two rays be point $P$. Thus,$\Delta PQR$ is formed.
$5$. Draw an acute angle $\angle RQX$ below the base $QR$.
$6$. Locate $4$ points $Q_1, Q_2, Q_3, Q_4$ on ray $QX$ such that $QQ_1 = Q_1Q_2 = Q_2Q_3 = Q_3Q_4$.
$7$. Join $Q_3$ to $R$. Draw a line through $Q_4$ parallel to $Q_3R$ intersecting the extended line segment $QR$ at $R'$.
$8$. Draw a line through $R'$ parallel to $RP$ intersecting the extended line segment $QP$ at $P'$.
$9$. $\Delta P'QR'$ is the required triangle similar to $\Delta PQR$ with a scale factor of $\frac{4}{3}$.
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