<p>In the diagram, angle \(BAC\) and angle \(ABD\) are right angles. \(AB = AC\), \(AF = \frac{2}{3} AB\) and \(BD = \frac{2}{3} AC\). \(AD\), \(CF\) intersect at \(E\). Prove that</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/1770110426114-ep9ztyick8t.png" style="max-width: min(160px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">triangles \(ACF\) and \(BAD\) are congruent, and</span></div></li><li><div class="list-item-content"><span class="list-item-text">triangles \(ACF\) and \(EAF\) are similar.</span></div></li></ol>

In the diagram, angle \(BAC\) and angle \(ABD\) are right angles. \(AB = AC\), \(AF = \frac{2}{3} AB\) and \(BD = \frac{2}{3} AC\). \(AD\), \(CF\) intersect at \(E\). Prove that

triangles \(ACF\) and \(BAD\) are congruent, and

triangles \(ACF\) and \(EAF\) are similar.

Proofs in Plane Geometry

Question 33bf2119