The image shows a geometric diagram involving parallel lines and a proof table. The proof table consists of statements and corresponding reasons, with the fifth statement missing its justification. Let's analyze the given information step by step:

Given Information:

1. $\overleftrightarrow{TV} \parallel \overleftrightarrow{FH}$ (Line $TV$ is parallel to line $FH$) - This is stated as a given.
2. $\overleftrightarrow{WY} \parallel \overleftrightarrow{FH}$ (Line $WY$ is parallel to line $FH$) - Also given.

Statements and Reasons:

• Statement 3: $\angle SUV \cong \angle HGS$

  • Reason: Corresponding Angles Theorem (Because $TV \parallel FH$).

• Statement 4: $\angle HGS \cong \angle WXZ$

  • Reason: Alternate Exterior Angles Theorem (Because $WY \parallel FH$).

Statement 5:

• $\angle SUV \cong \angle WXZ$

Reason for Statement 5:

The appropriate reason here would be the Transitive Property of Congruence. The transitive property states that if two angles are each congruent to a third angle, then they are congruent to each other. Since $\angle SUV \cong \angle HGS$ and $\angle HGS \cong \angle WXZ$, it follows that $\angle SUV \cong \angle WXZ$.

Thus, the reason for statement 5 is the Transitive Property of Congruence.

Would you like more details or have any questions?

Related Questions:

1. How does the Corresponding Angles Theorem apply in parallel line proofs?
2. Can you explain the Alternate Exterior Angles Theorem in more detail?
3. What is the difference between the Transitive Property of Congruence and Equality?
4. How would the proof change if the lines were not parallel?
5. Can this reasoning be applied to other geometric shapes or configurations?

Tip:

In geometry proofs involving parallel lines, always look for opportunities to use theorems like the Corresponding Angles, Alternate Interior/Exterior Angles, and Transitive Property to connect different angles.