Construct triangle PQR where PQ = 7.5 cm, PR = 9 cm, and angle QPR = 135 degrees. Then construct the locus of points equidistant from P and Q (L1) and the locus of points equidistant from P and R (L2)

So, $|PQ| = 7.5 \text{ cm}$.

• Extend the line segment QP to the left of P.
• Construct a $90^\circ$ angle at P, opening upwards from PQ.
• Bisect the angle formed by the $90^\circ$ line and the extended line (to the left of P). This bisection will give a $45^\circ$ angle. The angle from PQ to this bisector will be $90^\circ + 45^\circ = 135^\circ$.

So, $|PR| = 9 \text{ cm}$.

a) ii) Constructing Locus $L_1$

This line is $L_1$, the locus of points equidistant from P and Q.

a) iii) Constructing Locus $L_2$

This line is $L_2$, the locus of points equidistant from Q and R.

b) Locating point S

c) Joining SR

d) Measuring $\angle SRQ$ and $\angle PQR$

Since this is a construction problem, the final angle measurements depend on the accuracy of your physical drawing. You will need to measure these angles from your constructed diagram.