Construct a triangle similar to a given ΔXYZ with its sides equal to (3/4)th of the corresponding sides of ΔXYZ. Write the steps of construction.
Given that
Construct a $\triangle X Y Z$ of given data, Let $X Y=5 \mathrm{~cm}, Y Z=6 \mathrm{~cm}$ and $\angle Y=60^{\prime}$ and then a triangle similar to it whose sides are $(3 / 4)$ of the corresponding sides of $\triangle X Y Z$.
We follow the following steps to construct the given
Step of construction
Step: I- First of all we draw a line segment $X Y=5 \mathrm{~cm}$.
Step: II- With $Y$ as centre draw an angle $\angle Y=60^{\circ}$.
Step: III- With $Y$ as centre and radius $=Y Z=6 \mathrm{~cm}$, draw an arc.
Step: IV-Join $X Z$ to obtain $\triangle X Y Z$.
Step: V-Below $X Y$, makes an acute angle $\angle Y X P=60^{\circ}$.
Step: VI -Along $X P$, mark off four points $X_{1}, X_{2} X_{3}$ and $X_{4}$ such that $X X_{1}=X_{1} X_{2}=X_{2} X_{3}=X_{3} X_{4}$
Step: VII- Join $X_{4} Y$.
Step: VIII- Since we have to construct a triangle each of whose sides is $(3 / 4)^{\text {th }}$ of the corresponding sides of $\triangle X Y Z$.
So, we take three parts out of four equal parts on $X P$ from point $X_{3}$ draw $X_{3} Y^{\prime} \| X_{4} Y$, and meeting $X Y$ at $Y^{\prime}$.
Step: IX- From $Y^{\prime}$ draw $Y^{\prime} Z^{\prime} \| Y Z$, and meeting $X Z$ at $Z^{\prime}$
Thus, $\triangle X Y^{\prime} Z^{\prime}$ is the required triangle, each of whose sides is $(3 / 4)^{\text {th }}$ of the corresponding sides of $\triangle X Y Z$.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.