Valid Conclusion 68D86A

1. **State the problem:** We have two true conditional statements: - Statement 1: If a figure is a square, then it is a rectangle. - Statement 2: If a figure is a rectangle, then it is a parallelogram. We want to determine which conclusion among A, B, C, and D is valid. 2. **Recall the rule of transitivity for conditional statements:** If $P \to Q$ and $Q \to R$ are true, then $P \to R$ is also true. 3. **Apply the rule:** Let: - $P$: Figure A is a square. - $Q$: Figure A is a rectangle. - $R$: Figure A is a parallelogram. Given: - $P \to Q$ (Statement 1) - $Q \to R$ (Statement 2) By transitivity: $$P \to R$$ This means: If Figure A is a square, then Figure A is a parallelogram. 4. **Evaluate the options:** - A: If Figure A is a square, then Figure A is a parallelogram. **Valid** (matches $P \to R$). - B: If Figure A is not a square, then Figure A is not a parallelogram. **Invalid** (the contrapositive of $P \to R$ is If not $R$, then not $P$, not this). - C: If Figure A is a parallelogram, then Figure A is a square. **Invalid** (reverse of $P \to R$, not necessarily true). - D: If Figure A is a rectangle, then Figure A is a square. **Invalid** (reverse of $P \to Q$, not necessarily true). 5. **Final answer:** The valid conclusion is option A. **Answer:** A. If Figure A is a square, then Figure A is a parallelogram.