Video: Properties of Parallelograms

Which of the following statements must be true about a parallelogram? [A] It has four sides of equal length. [B] It has four right angles. [C] It has four congruent sides. [D] It has exactly one pair of parallel sides. [E] It has exactly two pairs of parallel sides.

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Video Transcript

Which of the following statements must be true about a parallelogram? Option (A) it has four sides of equal length. Option (B) it has four right angles. Option (C) it has four congruent sides. Option (D) it has exactly one pair of parallel sides. Or option (E) it has exactly two pairs of parallel sides.

In order to answer this question, we’ll need to remember what exactly a parallelogram is. It’s defined as a quadrilateral or four-sided shape, with both pairs of opposite sides parallel. We could therefore draw a range of different parallelograms. The important thing is that, in each one, it will have both pairs of opposite sides parallel. So let’s have a look at the different statements we’re given.

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. We could’ve drawn a square or even a rhombus, and that would have four sides of equal length. But we can’t say that about every single parallelogram. And so option (A) is incorrect.

Option (C) is phrased differently. It has the word congruent here, referring to the sides, which means that it’d say it would have four equal sides. We can see that this would not be the case. Option (B) says it has four right angles. Well, we know that a square or a rectangle does have four right angles, but it doesn’t apply to every single parallelogram. Therefore, option (B) isn’t correct. Option (D) says it has exactly one pair of parallel sides. 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). It has exactly two pairs of parallel sides.

The definition of a parallelogram tells us that both pairs or two pairs of the opposite sides will be parallel. So option (E) is our correct answer. It has exactly two pairs of parallel sides.

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