<p>In the diagram, \(AB\) is parallel to \(DC\), and \(AC\) and \(BD\) meet at \(X\).</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1767505865518-544hnzuacmw.png" style="max-width: min(270px, 100%); height: auto; display: block;" alt="Trapezium ABCD with diagonals AC and BD intersecting at point X. AB is 24 cm, AX is 12 cm, and XC is 18 cm." class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Prove that triangles \(\Delta ABX\) and \(\Delta CDX\) are similar.</span></div></li><li><div class="list-item-paragraph">Given that&nbsp;\(AB = 24\text{ cm}\), \(AX = 12\text{ cm}\) and \(XC = 18\text{ cm}\).</div><div class="list-item-paragraph">Find \(CD\).</div></li><li><div class="list-item-content"><span class="list-item-text">Given also that&nbsp;\(BD = 42\text{ cm}\), find \(BX\).</span></div></li><li><div class="list-item-paragraph">Find</div><ol class="abc-list"><li><div class="list-item-paragraph">\(\frac{\text{Area}\hspace{0.5em} \Delta ABX}{\text{Area}\hspace{0.5em} \Delta CDX}\) ,</div></li><li><div class="list-item-paragraph">\(\frac{\text{Area}\hspace{0.5em} \Delta ADX}{\text{Area}\hspace{0.5em} \Delta ACD}\) .</div></li></ol></li></ol>

In the diagram, \(AB\) is parallel to \(DC\), and \(AC\) and \(BD\) meet at \(X\).

Prove that triangles \(\Delta ABX\) and \(\Delta CDX\) are similar.

Given that \(AB = 24\text{ cm}\), \(AX = 12\text{ cm}\) and \(XC = 18\text{ cm}\).\n\nFind \(CD\).

Given that \(AB = 24\text{ cm}\), \(AX = 12\text{ cm}\) and \(XC = 18\text{ cm}\).

Given also that \(BD = 42\text{ cm}\), find \(BX\).

Find\n\n(a) \(\frac{\text{Area } \Delta ABX}{\text{Area } \Delta CDX}\) ,\n\n(b) \(\frac{\text{Area } \Delta ADX}{\text{Area } \Delta ACD}\) .

Problem involving Similar Figures

Problem involving Similar Figures

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