In parallelogram ABCD, D is a right angle. Is ABCD a rectangle?A.Cannot be determinedB.YesC.No

Break Down the Problem

1. Understanding Parallelogram: A parallelogram has opposite sides that are equal in length and opposite angles that are equal.
2. Right Angle At D: Since angle D is a right angle (90 degrees), we need to consider the implications for the other angles in the parallelogram.

Relevant Concepts

1. Properties of Parallelograms: In a parallelogram, if one angle is a right angle, then all angles must be right angles. This follows from the fact that opposite angles are equal, and adjacent angles are supplementary.
2. Definition of a Rectangle: A rectangle is a special type of parallelogram in which all angles are right angles.

Analysis and Detail

1. In parallelogram ABCD, if angle D is 90 degrees, then: $\text{Angle A} + \text{Angle D} = 180 \text{ degrees}$ $\text{Angle A} + 90 \text{ degrees} = 180 \text{ degrees}$ This means: $\text{Angle A} = 90 \text{ degrees}$
2. Similarly, since opposite angles are equal, angle B will also be 90 degrees, and angle C will be 90 degrees as well: $\text{Angle B} = \text{Angle D} = \text{Angle A} = \text{Angle C} = 90 \text{ degrees}$
3. Therefore, all angles in parallelogram ABCD are 90 degrees.

Verify and Summarize

Since all angles in parallelogram ABCD are right angles, it meets the definition of a rectangle.

Final Answer

B. Yes, parallelogram ABCD is a rectangle.