Question

step statement reason
1 (overline{ab}congoverline{cd})
(overline{fa}congoverline{ed})
(overline{fa}perpoverline{ad})
(overline{ed}perpoverline{ad}) given
2 (angle a) is a right angle perpendicular lines form right angles
3 (angle d) is a right angle perpendicular lines form right angles
4 (angle acongangle d) all right angles are congruent
5 (overline{bc}congoverline{bc}) reflexive property
6 (\triangle faccong\triangle) select a reason.
7 (\triangle faccong\triangle edb) sas

Explanation:

Step1: Identify corresponding parts

We have \(AB\cong CD\), \(FA\cong ED\), \(FA\perp AD\), \(ED\perp AD\), \(\angle A\cong\angle D\) (right angles), \(BC\cong BC\).

Step2: Determine the congruent triangle

For \(\triangle FAC\) and \(\triangle EDB\), we have \(FA = ED\) (given), \(\angle A=\angle D\) (right angles, so congruent), and \(AC=DB\) (since \(AB = CD\) and \(BC\) is common, \(AB + BC=CD + BC\) i.e. \(AC = DB\)).

Answer:

\(\triangle FAC\cong\triangle EDB\) by \(SAS\) (Side - Angle - Side)