Question

6 complete the proof: (use givens first) given: \\( \overline { a e } \parallel \overline { d c } \\) prove: \\( \triangle b f e \sim \triangle c f d \\) 1. \\( \overline { a e } \parallel \overline { d c } \\) 2.

Explanation:

Step1: Identify corresponding angles

Since \(\overline{AE}\parallel\overline{DC}\), by the property of parallel lines, \(\angle BEF=\angle FDC\) (alternate - interior angles) and \(\angle EBF=\angle FCD\) (alternate - interior angles).

Step2: Use AA (Angle - Angle) similarity criterion

In \(\triangle BFE\) and \(\triangle CFD\), we have two pairs of equal angles: \(\angle BEF=\angle FDC\) and \(\angle EBF=\angle FCD\). According to 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 AA similarity criterion)