Question

Draw $△ABC$, where $m\angle ABC={90}^o;BC=4cm$ and $AC=5cm$ and then construct $△BXY$ with $4/3$ scale factor. Write points of construction.

Answer 1

Data: Construct $△ABC$ with $m\angle ABC={90}^o$, $BC=4cm$ and $AC=5cm$
To Construct: Construct $△BXY$ similar to $△ABC$ where the scale factor is $\frac{4}{3}$
Steps of Construction:
(i) Construct $△ABC$ with $m\angle ABC={90}^o,BC=4cm$ and $AC=5cm$.
(ii) In the half plane of $\overline{BC}$ not containing $A$, draw $\overline{BN}$ such that $\angle CBN$ is an acute angle.
(iii) With some appropriate radius and centre $B$, draw an arc to intersect $\overline{BN}$ at $B_1$. With the same radius and centre $B_1$, draw and arc to intersect $BN$ at $B_2$ such that $B-B_1-B_2$.
Similarly, with the same radius and centre $B_k$, draw an arc to intersect $BN$ at $B_{k+1}$ such that $B_{k-1}-B-B_{k+1}$, where $k=2,3,....$
(iv) Draw $B_{3}C$
(v) Through $B_4$, draw a ray parallel to $B_{3}C$ to intersect $BC$ at $X$.
(vi) Through $X$, draw a ray parallel to $CA$ to intersect $BA$ at $Y$.
Thus $△BXY$ is the required triangle.