1. Construct triangle PQR with $PQ=6.5$ cm, $\angle PQR=105^\circ$, and $QR=8.0$ cm. Measure $PR$.\n\nStep 1: Draw segment $PQ=6.5$ cm using a ruler.\nStep 2: At point $Q$, use a protractor or compass to construct $\angle PQR=105^\circ$.\nStep 3: From $Q$, mark point $R$ on the ray forming the $105^\circ$ angle such that $QR=8.0$ cm.\nStep 4: Connect points $P$ and $R$ to complete triangle $PQR$.\nStep 5: Measure length $PR$ using the ruler.\n\n2. (a) Construct triangle QRT with $QR=8$ cm, $RT=6$ cm, and $QT=4.5$ cm.\nStep 1: Draw segment $QR=8$ cm.\nStep 2: With center $Q$ and radius $QT=4.5$ cm, draw an arc.\nStep 3: With center $R$ and radius $RT=6$ cm, draw another arc intersecting the first arc at point $T$.\nStep 4: Connect $Q$ to $T$ and $R$ to $T$ to form triangle $QRT$.\n\n(b) Construct quadrilateral QRSP sharing base $QR$ with triangle QRT such that $QTP$ is a straight line, $TP=4.5$ cm, $\angle QPS=120^\circ$, and $\angle PSR=90^\circ$.\nStep 1: Extend line $QT$ beyond $T$ to point $P$ such that $TP=4.5$ cm.\nStep 2: At point $P$, construct $\angle QPS=120^\circ$ using compass and ruler.\nStep 3: At point $S$, construct $\angle PSR=90^\circ$ such that $S$ lies on the rays from $P$ and $R$.\nStep 4: Connect points $P$ to $S$ and $S$ to $R$ to complete quadrilateral $QRSP$.\n\n(c) Measure length $PS$ using the ruler.\n\n3. Construct parallelogram ABCD with $AB=7.5$ cm, $\angle A=75^\circ$, and diagonal $AC=11.0$ cm. Measure $CD$.\nStep 1: Draw segment $AB=7.5$ cm.\nStep 2: At point $A$, construct $\angle BAD=75^\circ$.\nStep 3: Using compass, draw an arc with center $A$ and radius $AC=11.0$ cm intersecting the ray from $A$ at point $C$.\nStep 4: Draw segment $BC$ and complete parallelogram $ABCD$ by drawing $CD$ parallel and equal to $AB$, and $AD$ parallel and equal to $BC$.\nStep 5: Measure length $CD$.\n\n4. (a) Construct parallelogram ABCD with $AB=8$ cm, $\angle A=45^\circ$, and $\angle B=60^\circ$. Measure $CD$.\nStep 1: Draw segment $AB=8$ cm.\nStep 2: At point $A$, construct $\angle BAD=45^\circ$.\nStep 3: At point $B$, construct $\angle ABC=60^\circ$.\nStep 4: Complete parallelogram $ABCD$ by drawing $CD$ parallel to $AB$ and $AD$ parallel to $BC$.\nStep 5: Measure length $CD$.\n\n(b) Locate point $P$ inside triangle $ABC$ such that $AP=BP$ and $CP=4$ cm. Measure $PC$.\nStep 1: Construct triangle $ABC$.\nStep 2: Find the locus of points equidistant from $A$ and $B$ (the perpendicular bisector of $AB$).\nStep 3: Draw a circle centered at $C$ with radius $4$ cm.\nStep 4: Point $P$ is the intersection of the perpendicular bisector of $AB$ and the circle centered at $C$.\nStep 5: Measure length $PC$.\n\n5. Construct a regular hexagon with side length $7$ cm.\nStep 1: Draw a circle with radius $7$ cm.\nStep 2: Mark a point on the circle as the first vertex.\nStep 3: Using the compass set to $7$ cm, step around the circle marking six points.\nStep 4: Connect consecutive points to form the regular hexagon.