<p>The diagram shows two triangles \(ABE\) and \(ACD\), where&nbsp;\(AB = 3.5\text{ cm}\), \(BC = 2.1\text{ cm}\), \(AE = 3\text{ cm}\) and \(DE = 1.8\text{ cm}\).</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/1767499437975-ky67wehjwrk.png" style="max-width: min(320px, 100%); height: auto; display: block;" alt="Diagram of triangle ACD with an internal segment BE, showing side lengths." class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text"><strong>Without assuming that&nbsp;\(BE\) is parallel to \(CD\)</strong>, show that the triangle \(ABE\) is similar to triangle \(ACD\), stating your reasons clearly.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the length \(BE\), given that the length \(CD\) is \(8.4\text{ cm}\).</span></div></li></ol>

The diagram shows two triangles \(ABE\) and \(ACD\), where \(AB = 3.5\text{ cm}\), \(BC = 2.1\text{ cm}\), \(AE = 3\text{ cm}\) and \(DE = 1.8\text{ cm}\).

**Without assuming that \(BE\) is parallel to \(CD\)**, show that the triangle \(ABE\) is similar to triangle \(ACD\), stating your reasons clearly.

Geometric Similarity and Proportionality in Nested Triangles

Geometric Similarity and Proportionality in Nested Triangles

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