To construct triangle PQR and measure the lengths of PQ and PR:

Draw a straight line and mark a point Q on it. Using a ruler, measure $6 \text{ cm}$ from Q and mark point R. So, $QR = 6 \text{ cm}$.

• With R as the center, draw an arc of any convenient radius to intersect $QR$ at a point, say A.
• With A as the center and the same radius, draw another arc to intersect the first arc at a point, say B. $\angle BRQ = 60^\circ$.
• Bisect $\angle BRQ$. With A and B as centers, draw arcs of the same radius (larger than half the distance AB) to intersect at a point, say C.
• Draw a line from R through C. This line forms an angle of $30^\circ$ with $QR$.

• With Q as the center, draw an arc of any convenient radius to intersect $QR$ at a point, say D.
• With D as the center and the same radius, draw an arc to intersect the first arc at E ($60^\circ$).
• With E as the center and the same radius, draw an arc to intersect the first arc at F ($120^\circ$).
• Bisect the angle between E and F to construct $90^\circ$. With E and F as centers, draw arcs of the same radius to intersect at G.
• Draw a dashed line from Q through G. This line represents $90^\circ$. Let the intersection of this line with the initial arc be H.
• Now, bisect the angle between E ($60^\circ$) and H ($90^\circ$). With E and H as centers, draw arcs of the same radius to intersect at I.
• Draw a line from Q through I. This line forms an angle of $60^\circ + 15^\circ = 75^\circ$ with $QR$.

The intersection of the line from R (from Step 2) and the line from Q (from Step 3) is point P. Connect P to Q and P to R to complete triangle PQR.

Measurement of $|PQ|$ and $|PR|$:

Since physical measurement cannot be performed by an AI, we will calculate the lengths using trigonometry.

First, find the third angle $\angle QPR$:
The sum of angles in a triangle is $180^\circ$.

Since $\angle PQR = \angle QPR = 75^\circ$, triangle PQR is an isosceles triangle with sides opposite these angles being equal.
Therefore, $PR = QR$.
Given $QR = 6 \text{ cm}$,

Now, use the Sine Rule to find the length of $PQ$:

We know $\sin(30^\circ) = 0.5$ and $\sin(75^\circ) = \frac{\sqrt{6} + \sqrt{2}}{4} \approx 0.9659$.

Rounding to two decimal places:

The measured lengths are:
$|PQ| = \boxed{\text{3.11 cm}}$
$|PR| = \boxed{\text{6.00 cm}}$