![]() Similarly, \(\angle FCE\) and \(\angle DAE\) are the alternate interior angles.Īssume \(CF\) and \(AB\) are the two lines that are intersected by the transversal \(AC.\)Īnd \(CF = BD\) (since \(BD = AD,\) it is proved that \(CF = AD\)) \(\angle CFE\) and \(\angle ADE\) are the alternate interior angles as \(DA\parallel CF\) and \(DF\) is the transversal.Īssume \(CF\) and \(AB\) as two lines that are intersected by the transversal \(DF.\) \(\angle FCE = \angle DAE\) (by c.p.c.t.) ![]() \(\angle CFE = \angle ADE\) (by c.p.c.t.) We know that the corresponding parts of congruent triangles are equal. \(\angle CEF = \angle AED\) (These are vertically opposite angles as \(AC\) and \(DF\) intersects at point \(E\) and vertically opposite angles are equal) \(EC = AE\) (\(\because E\) is the midpoint of the side\(AC\)) Construction: Let us join \(E\) and \(D\) and extend the line segment \(DE\) and produce it to \(F\) such that, \(EF = DE.\)
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