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Which of the following statements must be true about a parallelogram?
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Option (A) it has four sides of equal length.
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Option (B) it has four right angles.
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Option (C) it has four congruent sides.
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Option (D) it has exactly one pair of parallel sides.
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Or option (E) it has exactly two pairs of parallel sides.
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In order to answer this question, we’ll need to remember what exactly a parallelogram is.
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It’s defined as a quadrilateral or four-sided shape, with both pairs of opposite sides parallel.
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We could therefore draw a range of different parallelograms.
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The important thing is that, in each one, it will have both pairs of opposite sides parallel.
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So let’s have a look at the different statements we’re given.
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Looking at option (A), which says it has four sides of equal length, we can see that the parallelograms we’ve drawn definitely don’t have four sides of equal length.
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We could’ve drawn a square or even a rhombus, and that would have four sides of equal length.
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But we can’t say that about every single parallelogram.
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And so option (A) is incorrect.
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Option (C) is phrased differently.
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It has the word congruent here, referring to the sides, which means that it’d say it would have four equal sides.
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We can see that this would not be the case.
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Option (B) says it has four right angles.
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Well, we know that a square or a rectangle does have four right angles, but it doesn’t apply to every single parallelogram.
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Therefore, option (B) isn’t correct.
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Option (D) says it has exactly one pair of parallel sides.
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Well, we know from the definition that both pairs of opposite sides have to be parallel, so option (D) is incorrect, which leaves us with option (E).
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It has exactly two pairs of parallel sides.
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The definition of a parallelogram tells us that both pairs or two pairs of the opposite sides will be parallel.
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So option (E) is our correct answer.
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It has exactly two pairs of parallel sides.