which of the following properties is/are common to parallelograms and rectangles? I. all angles are right…

Analyze the question: We need the properties that hold for both a general parallelogram and a rectangle. A rectangle is a special parallelogram, so a property must be true of every parallelogram to count as "common."

Check each statement:

• I. All angles are right angles. This is true only for rectangles. A general parallelogram has opposite angles equal, but they need not be 90°. So this is not common.
• II. The diagonals are equal. This is true for rectangles. In a general parallelogram the diagonals bisect each other but are usually unequal in length. So this is not common.
• III. Opposite sides are equal and parallel. This is the defining property of a parallelogram, and a rectangle has it too. So this is common.

Conclusion: Only statement III is common to both shapes.

Answer: E

Tip: A rectangle is a parallelogram with extra properties (right angles and equal diagonals). When a question asks what is common to both, pick only the properties of the general shape, here the parallelogram. Those extra properties belong to the rectangle alone.