Question

complete the proof.
given: $overline{fg}paralleloverline{kl}$, $overline{fg}congoverline{kl}$
prove: $\triangle fgkcong\triangle klf$
complete the proof below.

statement	reasons
2. $overline{fg}congoverline{kl}$	2. given
3. $overline{fk}congoverline{fk}$	3. reflexive property of $cong$
4. $angle gkfcongangle lfk$	4. vertical angle theorem
5. $\triangle fgkcong\triangle klf$	5. sas using 2, 3, and 4

Explanation:

Answer:

Discipline: Mathematics
Subfield: Geometry
Proof Completion:

Statement	Reasons
2. \(FG\cong KL\)	2. Given
3. \(FK\cong FK\)	3. Reflexive property of \(\cong\)
4. \(\angle GKF\cong\angle LFK\)	4. Alternate - Interior Angles Theorem (since \(FG\parallel KL\) and \(FK\) is a transversal)
5. \(\triangle FGK\cong\triangle KLF\)	5. SAS (Side - Angle - Side) using 2, 3, and 4