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Choose from the following statements the properties of a parallelogram: A) it has two pairs of opposite sides of equal length, B) it is a quadrilateral of four equal angles, C) it has one pair of perpendicular sides, D) it has four sides of equal length, E) it has two pairs of equal angles.
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Let’s write a definition of what we know to be true of a parallelogram.
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A parallelogram is a four-sided flat shape with straight sides, where opposite sides are parallel, opposite sides are equal in length, and opposite angles are equal.
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Based on this definition, let’s walk back through statements A through E to see which ones would be true.
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It has two pairs of opposite sides of equal length.
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Yes, that is true of a parallelogram.
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It is a quadrilateral of four equal angles.
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It is four-sided.
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So it is a quadrilateral.
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But opposite angles are equal.
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And sometimes that will mean all four angles are equal, for example, in a square.
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But that’s not always the case.
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So we can’t say that that is true.
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We can only say opposite angles are equal, not that all four angles are equal.
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It has one pair of perpendicular sides.
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Well, some parallelograms may have perpendicular sides.
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It’s not a requirement.
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Statement D, it has four sides of equal length.
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We know that can’t be true.
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A rectangle is a parallelogram.
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So it doesn’t have to have four sides of equal length to be a parallelogram.
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Opposite sides are equal in length, but not all four sides.
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So far, we still only have statement A that is always true.
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Final statement, statement E, it has two pairs of equal angles.
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This is true.
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Opposite angles are equal.
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And because it’s a quadrilateral, there will be two sets of angles.
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Opposite angles are equal.
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Two pairs of equal angles, that’s true.
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So we can say that statement A and statement E are true for all parallelograms.