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<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Construct a quadrilateral $ABCD$ such that $AB = 6.3$ cm, $AC = 8.2$ cm, $BD = 5.6$ cm, $AB$ is perpendicular to $BC$, and angle $BAD = 60^\circ$.</span></div><ol class="abc-list"><li><div class="list-item-paragraph">Measure and write down the largest possible size of angle $ADC$.</div></li><li><div class="list-item-paragraph">Construct a straight line parallel to $AB$ that passes through $C$ to meet $AD$ produced at $E$. Measure and write down the length of $CE$ and determine the type of quadrilateral $ABCE$.</div></li></ol></li></ol>
<ol class="i-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Construct a quadrilateral $ABCD$ such that $AB = 4.5$ cm, $BC = 4$ cm, $CD = 4.2$ cm, diagonal $BD = 3.4$ cm, angle $BAD = 40^\circ$ and angle $ADB$ is acute.</span></div><ol class="abc-list"><li><div class="list-item-paragraph">Measure and write down the length of $AC$.</div></li><li><div class="list-item-paragraph">Construct a point $P$ that lies on side $AD$, such that $P$ is equidistant from $A$ and $B$. Measure and write down the length of $PD$.</div></li></ol></li></ol>

Construct a quadrilateral $ABCD$ such that $AB = 6.3$ cm, $AC = 8.2$ cm, $BD = 5.6$ cm, $AB$ is perpendicular to $BC$, and angle $BAD = 60^\circ$.

Construct a quadrilateral $ABCD$ such that $AB = 4.5$ cm, $BC = 4$ cm, $CD = 4.2$ cm, diagonal $BD = 3.4$ cm, angle $BAD = 40^\circ$ and angle $ADB$ is acute.

Constructing Perpendicular Bisectors

Constructing Quadrilaterals

Loci and Regions by Construction

 Constructions of Quadrillaterals

Geometrical Constructions

<ol class="i-list"><li><div class="list-item-paragraph">Construct a parallelogram $ABCD$ such that&nbsp;$AB=11$ cm, $BC=8$ cm and angle $ABC=45^{\circ}$.<br>Measure and write down the length of the diagonal $AC$.</div></li><li><div class="list-item-paragraph">Construct a trapezium $ABCD$ such that&nbsp;$AD$ is parallel to $BC$, $AB=3.7$ cm, $BC=8.8$ cm, $CD=4.2$ cm and angle $ABC=60^{\circ}$.</div><div class="list-item-paragraph">Measure and write down the lengths of $AD$ and the diagonal $AC$.</div></li></ol>

Constructions of Quadrillaterals

<p>A quadrilateral $ABCD$ has&nbsp;$\angle BAD=115{}^\circ $, $AB=7$ cm, $AD=5$ cm, $BC=8$ cm and $CD=10$ cm.</p>
<ol class="abc-list"><li data-list-item-id="item-1764331388209-kcpfai665"><div class="list-item-paragraph">Complete accurately the quadrilateral $ABCD$ in the space above.<br><br><br><br><br><br><br><br><br><br><br><br></div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1764331399193-zmkna5d7bh.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQzMzEzOTkxOTMtem1rbmE1ZDdiaC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyODgxLCJleHAiOjE3OTI2NjMxODF9.5mcyIEFqwlmB35aB6Mw-IBtaq6yLWAV31U7tokVuAC4" alt="List item image" class="aligncenter custom-width" style="max-width: min(320px, 100%); height: auto;" /></div><div class="list-item-paragraph"><br><br><br><br><br><br><br><br><br><br></div></li><li data-list-item-id="item-1764331407972-xdu27hk6f"><div class="list-item-paragraph">Measure and write down the $\angle BCD$.</div></li><li data-list-item-id="item-1764331416986-cf38cpp5j"><div class="list-item-paragraph">Construct</div><ol class="i-list"><li data-list-item-id="subitem-1764331425168-hbkw9l3bj"><div class="list-item-paragraph">the perpendicular bisector of $AB$,</div></li><li data-list-item-id="subitem-1764331427725-7jnki4720"><div class="list-item-paragraph">the angle bisector of $\angle BAD$.</div></li></ol></li><li data-list-item-id="item-1764331452926-28whpiiex"><div class="list-item-paragraph">The perpendicular bisector of $AB$ meets the angle bisector of $\angle BAD$ at $E$.  Mark the<br>point $E$ and write down the length of $AE$.<br></div></li></ol>

A quadrilateral $ABCD$ has $\angle BAD=115{}^\circ $, $AB=7$ cm, $AD=5$ cm, $BC=8$ cm and $CD=10$ cm.

Constructing Angle Bisectors

Geometry Constructions: Bisectors in a Quadrilateral

<ol class="abc-list"><li><div class="list-item-paragraph">Construct a quadrilateral $ABCD$ such that&nbsp;$AB=9$ cm, $AD=8$ cm, $BC=6$ cm,$\angle BAD=60{}^\circ $ and $\angle ABC=90{}^\circ $.  </div></li><li><div class="list-item-paragraph">Construct</div><ol class="i-list"><li><div class="list-item-paragraph">the perpendicular bisector of $AD$,</div></li><li><div class="list-item-paragraph">the bisector of $\angle BAD$.</div></li></ol></li><li><div class="list-item-paragraph">A point $P$ is equidistant from $AD$ and $AB$, and is also nearer to $A$ than $D$. Mark and label clearly a possible point $P$.</div></li></ol>

Quadrilateral Construction and Locus Conditions

<ol class="abc-list"><li><div class="list-item-paragraph">Construct quadrilateral $ABCD$ where&nbsp;$AB=12$ cm, $BC=6$ cm, $\angle ABC=90{}^\circ $, $CD=10.5$ cm and $AD=11.4$ cm. </div></li><li><div class="list-item-paragraph">Construct</div><ol class="i-list"><li><div class="list-item-paragraph">the perpendicular bisector of $CD$,</div></li><li><div class="list-item-paragraph">the angle bisector of $\angle ABC$.</div></li></ol></li><li><div class="list-item-paragraph">Mark clearly a possible point which is inside the quadrilateral, equidistant to the points $C$ and $D$, and is nearer to lines $AB$ than $BC$. Label this point $K$.</div></li></ol>

Quadrilateral Construction and Loci

<p>Construct a quadrilateral $ABCD$ such that&nbsp;$AB=4.5$ cm, $BC=7$ cm, $CD=6$ cm, $AD=5$ cm and the diagonal $AC=8$ cm. Measure and write down the size of angle $ADC$.</p>

Construct a quadrilateral $ABCD$ such that $AB=4.5$ cm, $BC=7$ cm, $CD=6$ cm, $AD=5$ cm and the diagonal $AC=8$ cm. Measure and write down the size of angle $ADC$.

Quadrilateral Construction with Given Side Lengths

<p>Construct a quadrilateral $ABCD$ such that&nbsp;$AB=7.5$ cm, $BC=8$ cm, $CD=6.8$ cm, $AD=4.7$ cm and the diagonal $AC=11$ cm. Measure and write down the size of angle $ACD$.</p>

Construct a quadrilateral $ABCD$ such that $AB=7.5$ cm, $BC=8$ cm, $CD=6.8$ cm, $AD=4.7$ cm and the diagonal $AC=11$ cm. Measure and write down the size of angle $ACD$.

<p>Construct the parallelogram $ABCD$ given the $2$ adjacent sides $AB$ and $BC$ below.</p>
<p>Hence construct the perpendicular bisector of the line $BD$.<br><br><br><br><br><br><br></p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1764329137578-ed9hwpmhwt.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQzMjkxMzc1NzgtZWQ5aHdwbWh3dC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyODgxLCJleHAiOjE3OTI2NjMxODF9.XiXlzeKtmX3f8yzO-uAeOhKnkMgGyektJ2iycuLTvuE" style="max-width: min(350px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

Construct the parallelogram $ABCD$ given the $2$ adjacent sides $AB$ and $BC$ below.

Hence construct the perpendicular bisector of the line $BD$.








Parallelogram Construction and Perpendicular Bisector

<ol class="abc-list"><li><div class="list-item-paragraph">Construct, and label a parallelogram $ABCD$ in which $AB=10$ cm, $AD=4$ cm and angle $BAD=75{}^\circ $.</div></li><li><div class="list-item-paragraph">Construct the angle bisector of angle $ADC$.</div></li><li><div class="list-item-paragraph">Construct the perpendicular bisector of $DC$.</div></li><li><div class="list-item-paragraph">Mark the point at which the angle bisector of angle $ADC$ intersect the perpendicular 	bisector of $DC$ as&nbsp;$X$ and hence measure the reflex angle $AXB$.</div></li></ol>

Parallelogram Construction and Bisectors

<p>Construct a quadrilateral $ABCD$ given&nbsp;$AB=6$ cm, $A\hat{B}C=65{}^\circ $, $BD=8$ cm, $B\hat{A}D=110{}^\circ $ and $A\hat{D}C=95{}^\circ $. On the same diagram, construct</p>
<ol class="abc-list"><li><div class="list-item-paragraph">the bisector of angle $BCD$,</div></li><li><div class="list-item-paragraph">the perpendicular bisector of $BC$.</div></li></ol>

Construct a quadrilateral $ABCD$ given $AB=6$ cm, $A\hat{B}C=65{}^\circ $, $BD=8$ cm, $B\hat{A}D=110{}^\circ $ and $A\hat{D}C=95{}^\circ $. On the same diagram, construct

Construction of Quadrilateral

<ol class="abc-list"><li><div class="list-item-paragraph">Construct a parallelogram $ABCD$ such that, $AB=8$ cm, $BC=6.3$ cm and angle$ABC=62{}^\circ $.</div></li><li><div class="list-item-paragraph">Measure and write down the length of diagonal $AC$. </div></li></ol>

Construction of a Parallelogram

<p>Quadrilateral ${ABCD}$ is such that ${AB = 10\ \mathrm{cm}}$, ${BC = 12\ \mathrm{cm}}$, ${AD = 10.5\ \mathrm{cm}}$, ${CD = 7\ \mathrm{cm}}$ and angle ${ABC = 70^\circ}$</p>
<p>The line ${AB}$ has been drawn in the answer space below.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Construct quadrilateral ${ABCD}$.</div><p style="text-align: right;">[3]</p></li><li><div class="list-item-paragraph">Measure and write down angle ${BCD}$.</div><p style="text-align: right;">[1]</p></li></ol>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1760333860794-r8w9kejqa8g.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjAzMzM4NjA3OTQtcjh3OWtlanFhOGcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjg4MSwiZXhwIjoxNzkyNjYzMTgxfQ.yr-DSOfEhL0oFCOZct97Xs35wXGxjT0c2IUt4FSOrfs" width="400" class="aligncenter" /></figure>

Quadrilateral ${ABCD}$ is such that ${AB = 10\ \mathrm{cm}}$, ${BC = 12\ \mathrm{cm}}$, ${AD = 10.5\ \mathrm{cm}}$, ${CD = 7\ \mathrm{cm}}$ and angle ${ABC = 70^\circ}$

The line ${AB}$ has been drawn in the answer space below.

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