Question

1. List the properties of a parallelogram

2. Is it possible for a trapezoid to be a parallelogram? Why or why not?
2a. Could a rhombus be a square? Why or why not?

Answer 1

`\displaystyle 2b.` A rhombus can never be a square because although opposite interiour angles and all four sides are congruent, their interiour angles are not right angles.

`\displaystyle 2a.` A trapezium is impossibly a parallelogram because a parallelogram has two pairs of parallel sides.

`\displaystyle 1.` Convex polygon with two pairs of opposite sides that are parallel and congruent [equal in length (see above picture)]

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Answer 2

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Answer:

1. see the list below
2. no
3. yes

Explanation:

1. The dictionary definition of a parallelogram is ...

a quadrilateral with opposite sides parallel

As a consequence of this condition, a number of additional properties arise:

• opposite sides are the same length
• opposite angles are congruent
• adjacent angles are supplementary
• diagonals bisect each other

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2. The dictionary definition of a trapezoid (US; trapezium, UK) is ...

a quadrilateral with one pair of parallel sides.

As a consequence of this condition, it is not possible for a trapezoid to be a parallelogram.

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3. A rhombus is a special case of parallelogram in which all sides are the same length. A square is a special case of rhombus in which all angles are congruent (as are the diagonals). Yes, a rhombus may be a square.