QuestionEvaluate these statements about parallelograms: a) 6 sides? b) Opposite sides parallel? c) 1 or 2 pairs parallel? d) All sides equal?
Studdy Solution
STEP 1
Assumptions1. We are dealing with a parallelogram, a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. . The properties of a parallelogram are well-defined and universally accepted.
STEP 2
Statement a A parallelogram has six sides.
This statement is incorrect. By definition, a parallelogram is a quadrilateral, meaning it has four sides.
STEP 3
Statement b Opposite sides of a parallelogram are parallel.
This statement is correct. By definition, a parallelogram is a quadrilateral with both pairs of opposite sides parallel.
STEP 4
Statement c A parallelogram can have one pair or two pairs of parallel sides.
This statement is partially correct. A parallelogram must have two pairs of parallel sides. If it only had one pair of parallel sides, it would not be a parallelogram but a trapezoid.
STEP 5
Statement d All sides of a parallelogram have the same length.
This statement is incorrect. In a parallelogram, opposite sides are of equal length, but adjacent sides can be of different lengths. If all sides were of the same length, it would be a special type of parallelogram known as a rhombus.
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