MathDB
Quadrilateral

Source:

January 11, 2009

Problem Statement

Let ABCD ABCD be a quadrilateral with AB AB extended to E E so that \overline{AB} \equal{} \overline{BE}. Lines AC AC and CE CE are drawn to form angle ACE ACE. For this angle to be a right angle it is necessary that quadrilateral ABCD ABCD have: <spanclass=latexbold>(A)</span> all angles equal <span class='latex-bold'>(A)</span>\ \text{all angles equal} <spanclass=latexbold>(B)</span> all sides equal <span class='latex-bold'>(B)</span>\ \text{all sides equal} <spanclass=latexbold>(C)</span> two pairs of equal sides <span class='latex-bold'>(C)</span>\ \text{two pairs of equal sides} <spanclass=latexbold>(D)</span> one pair of equal sides <span class='latex-bold'>(D)</span>\ \text{one pair of equal sides} <spanclass=latexbold>(E)</span> one pair of equal angles <span class='latex-bold'>(E)</span>\ \text{one pair of equal angles}