Question

Construct a triangle similar to a given triangle $PQR$ with its sides equal to $\frac{2}{3}$ of the corresponding sides of the triangle $PQR$ (scale factor $\frac{2}{3}<1$ )

Answer 1

Steps of construction:
(i) Construct a $△PQR$ with any measurement.
(ii) Draw a ray $QX$ making an acute angle with $QR$ on the side opposite to the vertex $P$.
(iii) Locate 3 points $Q_1,Q_2$ and $Q_3$ on $QX$.
So that ${QQ}_1=Q_1{Q}_2=Q_2{Q}_3$
(iv) Join $Q_{3}R$ and draw a line through $Q_2$ parallel to $Q_{3}R$ to intersect $QR$ at $R^{\prime }$.
(v) Draw a line through $R^{\prime }$ parallel to the line $RP$ to intersect $QP$ at $P^{\prime }$. Then $△P^{\prime }Q{R}^{\prime }$ is the required triangle.