1. **Problem Statement:** Construct triangle PQR where $PQ=4.5$ cm, $QR=5.2$ cm, and angle $PQR=45^\circ$. 2. **Formula and Rules:** To construct a triangle given two sides and the included angle (SAS), we use the following steps: - Draw side $PQ$ of length 4.5 cm. - At point $Q$, construct an angle of $45^\circ$. - From $Q$, measure 5.2 cm along the ray forming the $45^\circ$ angle to locate point $R$. - Connect points $P$ and $R$ to complete the triangle. 3. **Step-by-step Construction:** - Draw segment $PQ$ = 4.5 cm. - At $Q$, use a protractor to draw a $45^\circ$ angle. - Along the ray from $Q$ at $45^\circ$, mark point $R$ such that $QR=5.2$ cm. - Draw segment $PR$ to complete triangle $PQR$. 4. **Explanation:** This method uses the SAS (Side-Angle-Side) triangle construction rule, which guarantees a unique triangle. 5. **Summary:** Triangle $PQR$ is constructed with $PQ=4.5$ cm, $QR=5.2$ cm, and angle $PQR=45^\circ$ by drawing side $PQ$, constructing the angle at $Q$, and marking $R$ accordingly. Final answer: Triangle $PQR$ constructed as described.