Question

statements 1 and 2 are true conditional statements. statement 1: if a figure is a parallelogram, then it is a quadrilateral. statement 2: if a figure is a quadrilateral, then its angles sum to 360°. which conclusion is valid? a) if figure a is a quadrilateral, then figure a is a parallelogram. b) if figure a is not a parallelogram, then figure as angles do not sum to 360°. c) if figure as angles do sum to 360°, then figure a is a parallelogram. d) if figure a is a parallelogram, then figure as angles sum to 360°.

Explanation:

Step1: Recall properties of quadrilaterals and parallelograms

A parallelogram is a type of quadrilateral. The sum of the interior - angles of any quadrilateral is 360°.

Step2: Analyze Statement 1

Statement 1: If a figure is a parallelogram, then it is a quadrilateral. This is true because by definition, a parallelogram has 4 sides, and a four - sided figure is a quadrilateral.

Step3: Analyze Statement 2

Statement 2: If a figure is a quadrilateral, then its angles sum to 360°. This is true as it is a well - known property of quadrilaterals.

Step4: Analyze Option A

Option A: If Figure A is a quadrilateral, then Figure A is a parallelogram. This is false because not all quadrilaterals are parallelograms. For example, a trapezoid is a quadrilateral but not a parallelogram.

Step5: Analyze Option B

Option B: If Figure A is not a parallelogram, then Figure A's angles do not sum to 360°. This is false because non - parallelogram quadrilaterals (like trapezoids, kites) still have angle sums of 360°.

Step6: Analyze Option C

Option C: If Figure A's angles sum to 360°, then Figure A is a parallelogram. This is false because there are many non - parallelogram quadrilaterals with angle sums of 360°.

Step7: Analyze Option D

Option D: If Figure A is a parallelogram, then Figure A's angles sum to 360°. Since a parallelogram is a quadrilateral and the sum of the angles of a quadrilateral is 360°, this statement is valid.

Answer:

D. If Figure A is a parallelogram, then Figure A's angles sum to 360°.