QUESTION IMAGE
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 |
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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 |