Question
Construct a triangle similar to a given triangle $A B C$ with its sides equal to $\frac{6}{5}$ of the corresponding sides of the triangle $ABC$ (scale factor $\frac{6}{5}>1$ )
✓
Answer
Given triangle $\triangle A B C$, we are required to construct another triangle whose sides are $\frac{6}{5}$ of the corresponding sides of the $\triangle A B C$.
Steps of construction:
(i) Construct an $\triangle ABC$ with any measurement.
(ii) Draw a ray $BX$ making an acute angle with $BC$.
(iii) Locate 6 points $Q _1, Q _2, Q _3, Q _4, Q _5, Q _6$ on $B X$ such that $B Q_1=Q_1 Q_2=Q_2 Q_3=Q_3 Q_4=Q_5 Q_6$
(iv) Join $Q_5$ to $C$ and draw a line through $Q_6$ parallel to $Q_5 C$ intersecting the extended line $BC$ at $C ^{\prime}$.
(v) Draw a line through $C^{\prime}$ parallel to $A C$ intersecting the extended line segment $A B$ at $A^{\prime}$.
$\therefore \triangle A ^{\prime} B C ^{\prime}$ is the required triangle.
Steps of construction:
(i) Construct an $\triangle ABC$ with any measurement.
(ii) Draw a ray $BX$ making an acute angle with $BC$.
(iii) Locate 6 points $Q _1, Q _2, Q _3, Q _4, Q _5, Q _6$ on $B X$ such that $B Q_1=Q_1 Q_2=Q_2 Q_3=Q_3 Q_4=Q_5 Q_6$
(iv) Join $Q_5$ to $C$ and draw a line through $Q_6$ parallel to $Q_5 C$ intersecting the extended line $BC$ at $C ^{\prime}$.
(v) Draw a line through $C^{\prime}$ parallel to $A C$ intersecting the extended line segment $A B$ at $A^{\prime}$.
$\therefore \triangle A ^{\prime} B C ^{\prime}$ is the required triangle.
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