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.
