Question

$\triangle SHR \sim \triangle SVU$. In $\triangle SHR$, $SH = 4.5$ cm, $HR = 5.2$ cm, and $SR = 5.8$ cm. If $\dfrac{SH}{SV} = \dfrac{3}{5}$, construct $\triangle SVU$.

Hint:

When constructing similar triangles, use the ratio of corresponding sides and draw parallel lines to maintain proportionality.

Answer 1

Step 1: Draw a line segment $HR = 5.2$ cm.
Step 2: With center $H$ and radius $4.5$ cm, draw an arc.
Step 3: With center $R$ and radius $5.8$ cm, draw another arc intersecting the first arc at point $S$. Join $S$ to $H$ and $S$ to $R$. Thus, $\triangle SHR$ is obtained.
Step 4: Extend $HS$ beyond $S$.
Step 5: From $H$, draw a ray $HX$ below $HS$. On $HX$, mark 5 equal divisions (since denominator of ratio is 5).
Step 6: Join the 3rd division point (since numerator of ratio is 3) to $S$. Draw a line through this point parallel to $SR$ to meet the extended $HS$ at point $V$.
Step 7: Through $V$, draw a line parallel to $HR$ meeting the extended $R$ line at $U$.
Step 8: $\triangle SVU$ is the required triangle similar to $\triangle SHR$.
Result: The required triangle $\triangle SVU$ is constructed such that $\triangle SHR \sim \triangle SVU$.