Is a rectangle a parallelogram always, sometimes or never?
2 Answers
Always.
Explanation:
For this question, all you need to know are the properties of each shape.
The properties of a rectangle are
- 4 right angles
- 4 sides (Polygonal)
- 2 pairs of opposite congruent sides
- congruent diagonals
- 2 sets parallel sides
- mutually bisecting diagonals
The properties of a parallelogram are
- 4 sides
- 2 pairs opposite congruent sides
- 2 sets of parallel sides
- both pairs opposite angles are congruent
- mutually bisecting diagonals
Since the question is asking if a rectangle is a parallelogram, you would check to make sure all the properties of the parallelogram agree with those of a rectangle and since they all do, the answer is always.
Any rectangle is a parallelogram
Explanation:
We have to start with definitions of a parallelogram and a rectangle.
DEFINITION of PARALLELOGRAM:
A quadrilateral (a polygon with 4 vertices)
DEFINITION of RECTANGLE:
A parallelogram with all 4 interior angles congruent to each other is called a rectangle.
So, straight from a definition we see that any rectangle is a parallelogram with additional property of having all interior angle congruent to each other.
NOTE:
There are different definitions of a rectangle, all equivalent to each other. In some cases the definition does not explicitly include the fact that it is, firstly, a parallelogram. Instead, the definition might specify that there are four sides and all interior angle are right angles. But, whatever the definition is, from it immediately follows that any rectangle is a parallelogram. If you find such a definition, an easy proof will be sufficient to show that a rectangle is a parallelogram.