<p>In the diagram, \(E\), \(F\), \(G\) and \(H\) are the midpoints of the sides of the rectangle \(ABCD\). The points \(P\), \(Q\), \(R\) and \(S\) are the midpoints of \(HE\), \(EF\), \(FG\) and \(GH\) respectively. By drawing the line segments \(EG\) and \(HF\), prove that</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">\(EF = EH\),</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(EFGH\) is a rhombus,</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(\angle SPQ = 90{}^\circ\),</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(PQRS\) is a rectangle.</span></div></li></ol>
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In the diagram, \(E\), \(F\), \(G\) and \(H\) are the midpoints of the sides of the rectangle \(ABCD\). The points \(P\), \(Q\), \(R\) and \(S\) are the midpoints of \(HE\), \(EF\), \(FG\) and \(GH\) respectively. By drawing the line segments \(EG\) and \(HF\), prove that

Proofs in Plane Geometry

Question 1ecd800f

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