Question

Construct a triangle similar to a given triangle $PQR$ with its sides equal to $2/3$ of the corresponding sides of the triangle PQR (scale factor $2/3$). (10 marks)

Answer 1

Given a triangle $PQR$, we are required to construct another triangle whose sides $2/3$ are of the corresponding sides of the triangle $PQR$.

Step of construction:

(1) Draw any ray $QX$ making an acute angle with $QR$ on the side opposite to the vertex $P$. [1 mark]

(2) Locate $3$ (the greater of $2$ and $3$ in $2/3$) points.
$Q1,Q2,Q3$ on $QX$ so that $QQ1=Q1Q2=Q2Q3$ [1 mark]

(3) Join $Q3R$ and draw a line through $Q2$ (the second point, $2$ being smaller of $2$ and $3$ in $2/3)$ parallel to $Q3R$ to intersect $QR$ at $R^{\prime }$ [1 mark]

(4) Draw a line through $R^{\prime }$ parallel to the line $RP$ to intersect $QP$ at $P^{\prime }$ [1 mark]

The $\Delta P^{\prime }Q{R}^{\prime }$ is the requried triangle each of whose sides is $2/3$ of the corresponding sides of $\Delta PQR$ [1 mark]


[5 marks]