complete the proof.
given: $ \overline { f g } \| \overline { k l }, \overline { f g } \cong \overline { k l } $
prove: $ \triangle f g k \cong \triangle k l f $
complete the proof below.
| statement | reasons |
| :---: | :---: |
| 1. $ \overline { f g } \| \overline { k l } $ | 1. given |
| 2. $ \overline { f g } \cong \overline { k l } $ | 2. given |
| 3. $ \overline { f k } \cong \overline { f k } $ | 3. reflexive property of $ \cong $ |
| 4. | 4. |
$ \angle f g k \cong \angle k l f $
$ \angle g f k \cong \angle l k f $
$ \angle g k f \cong \angle l f k $
$ \overline { f l } \cong \overline { k g } $

Question

Accepted Answer

# Explanation:
## Step1: Use the property of parallel lines
When $FG\parallel KL$, the alternate - interior angles are equal. So, $\angle GFK\cong\angle LKF$ (because $FG\parallel KL$ and $FK$ is a transversal, alternate - interior angles theorem).

## Step2: Prove the congruence of triangles
We have $FG\cong KL$ (given), $FK\cong FK$ (reflexive property of congruence), and $\angle GFK\cong\angle LKF$ (from step 1). By the Side - Angle - Side (SAS) congruence criterion, $\triangle FGK\cong\triangle KLF$.

# Answer:
4. $\angle GFK\cong\angle LKF$; 4. Alternate - interior angles theorem (since $FG\parallel KL$ and $FK$ is a transversal)

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of parallel lines

Step2: Prove the congruence of triangles

Answer:

statement	reasons
2. \\( \overline { f g } \cong \overline { k l } \\)	2. given
3. \\( \overline { f k } \cong \overline { f k } \\)	3. reflexive property of \\( \cong \\)
4.	4.