Let's analyze the image and break it down step by step to help answer the questions. Here's a summary of the key sections from the problem:

Part A

It asks which reason justifies the statement for Step 3 in the proof:

• Statement: $\angle PQS \cong \angle RSQ$ and $\angle QPR \cong \angle SRP$.
• This corresponds to angles being congruent because of alternate interior angles.

The correct answer for Part A is: D - "When two parallel lines are intersected by a transversal, alternate interior angles are congruent."

Part B

It asks which statement is justified by the reason for Step 4 in the proof:

• The reason provided is: "Opposite sides of a parallelogram are congruent."
• The corresponding statement involves the equality of opposite sides in the parallelogram.

The correct answer for Part B is: A - $PQ = RS$.

Part C

It asks which reason justifies Step 5 in the proof:

• The statement in Step 5 is: $\triangle SRT \cong \triangle QPT$.
• This congruence is based on the Side-Angle-Side (SAS) Triangle Congruence theorem.

The correct answer for Part C is: A - "Side-Angle-Side triangle congruence."

Final Summary

• Part A: D - Alternate interior angles are congruent.
• Part B: A - $PQ = RS$.
• Part C: A - Side-Angle-Side triangle congruence.

Would you like a more detailed explanation of any step or help with related concepts?

5 Related Questions:

1. Why are alternate interior angles congruent when a transversal crosses parallel lines?
2. What is the significance of SAS in proving triangle congruence?
3. How can you distinguish between SAS and other triangle congruence criteria?
4. Why do opposite sides of a parallelogram have to be congruent?
5. How can you generalize this proof method to other quadrilaterals, like rectangles or rhombuses?

One Tip:

When solving geometric proofs, always start by identifying given properties of the shape (like being a parallelogram) and use them systematically to reach your conclusion.