Question

complete the proof: (use givens first)
given: ( overline { a e } parallel overline { d c } )
prove: ( \triangle b f e sim \triangle c f d )

Explanation:

Step1: Use the property of parallel lines

Since \(\overline{AE}\parallel\overline{DC}\), we have \(\angle BEF=\angle DCF\) (alternate - interior angles) and \(\angle BFE=\angle CFD\) (vertical angles).

Step2: Apply the AA (Angle - Angle) similarity criterion

In \(\triangle BFE\) and \(\triangle CFD\), we have two pairs of equal angles: \(\angle BEF=\angle DCF\) and \(\angle BFE = \angle CFD\). By the AA similarity criterion, if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Answer:

\(\triangle BFE\sim\triangle CFD\) by the AA (Angle - Angle) similarity criterion.