$$ 4 x $$ If $$ O Q $$ and $$ R T $$ are parallel lines which statement is true? $$ 4 imes \quad $$ A $$ \angle R S P \cong \angle R S U $$ $$ 4 imes \quad $$ C $$ \angle R S P \cong \angle P S T $$ $$ 4 imes \quad \cap \quad \angle R S P \cong \angle O P S $$

Question

$$ 4 x $$ If $$ O Q $$ and $$ R T $$ are parallel lines which statement is true? $$ 4 	imes \quad $$ A $$ \angle R S P \cong \angle R S U $$ $$ 4 	imes \quad $$ C $$ \angle R S P \cong \angle P S T $$ $$ 4 	imes \quad \cap \quad \angle R S P \cong \angle O P S $$

UpStudy AI · Accepted Answer

To determine which statement is true given that $$ OQ $$ and $$ RT $$ are parallel lines, let's analyze the angle relationships formed by a transversal intersecting these parallel lines.

**Understanding the Scenario:**

- **Parallel Lines:** $$ OQ \parallel RT $$
- **Transversal:** A line that intersects both $$ OQ $$ and $$ RT $$, creating various angles at the points of intersection.

**Possible Angle Relationships:**

1. **Corresponding Angles:** These are angles that are in the same relative position at each intersection where the transversal crosses the parallel lines. Corresponding angles are equal ($$\cong$$).

2. **Alternate Interior Angles:** These are pairs of angles on opposite sides of the transversal but inside the two lines. They are equal ($$\cong$$).

3. **Alternate Exterior Angles:** Similar to alternate interior angles but located outside the parallel lines. They are also equal ($$\cong$$).

4. **Same-Side Interior Angles:** These angles are on the same side of the transversal and inside the parallel lines. They are supplementary (their measures add up to $$180^\circ$$).

**Analyzing the Options:**

Let's consider the given options:

- **Option A:** $$ \angle RSP \cong \angle RSU $$
  
  Without a diagram, it's unclear how these angles are positioned, but typically, $$ \angle RSP $$ and $$ \angle RSU $$ might not represent a standard pair like corresponding or alternate interior angles.

- **Option C:** $$ \angle RSP \cong \angle PST $$
  
  This is likely representing alternate interior angles formed by the transversal intersecting the parallel lines $$ OQ $$ and $$ RT $$. According to the properties of parallel lines, alternate interior angles are equal.

- **Option (Incomplete/Other):** $$ \angle RSP \cong \angle OPS $$
  
  This option seems incomplete or incorrectly formatted, making it difficult to assess its validity.

**Conclusion:**

Based on the properties of parallel lines and the typical angle relationships formed by a transversal, **Option C** ($$ \angle RSP \cong \angle PST $$) is the most plausible correct statement.

**Answer:**  
Option C: $$ \angle R S P \cong \angle P S T $$ is the true statement.
$$ \angle R S P \cong \angle P S T $$ is true.

\( 4 x \) If \( O Q \) and \( R T \) are parallel lines which statement is true? \( 4 \times \quad \) A \( \angle R S P \cong \angle R S U \) \( 4 \times \quad \) C \( \angle R S P \cong \angle P S T \) \( 4 \times \quad \cap \quad \angle R S P \cong \angle O P S \)

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