If RQRS is a parallelogram with two adjacent congruent sides then____ A.must be a rhombus B.might be a rhombus C.cannot be a rhombus
The Correct Answer and Explanation is:
The correct answer is B. might be a rhombus.
A parallelogram with two adjacent congruent sides has the potential to be a rhombus, but it isn’t necessarily a rhombus in all cases.
Here’s the explanation:
- Definition of a Parallelogram: A parallelogram is a quadrilateral where opposite sides are parallel and equal in length. In this case, RQRS is a parallelogram.
- Congruent Adjacent Sides: If two adjacent sides of the parallelogram (RQ and RS) are congruent, we now know that RQ=RSRQ = RSRQ=RS.
- Rhombus Definition: A rhombus is a special type of parallelogram where all four sides are congruent. So, if all four sides of the parallelogram RQRS are congruent, it would indeed be a rhombus.
- Can It Be a Rhombus?:
- Yes, it might be a rhombus. If the other two sides (QR and SR) are also congruent, then all four sides will be equal, making it a rhombus.
- No, it’s not guaranteed to be a rhombus. A parallelogram with two adjacent congruent sides might not have all four sides equal. For example, if the angles between the sides are not 90 degrees, the sides might be congruent but the figure will still be a general parallelogram, not a rhombus.
Thus, the parallelogram might be a rhombus, but it isn’t always one. Therefore, the correct answer is B. might be a rhombus.
