### Video Transcript

Are the two polygons similar?

Letโs begin by recalling what we
mean by the word โsimilar.โ We say that two polygons are
similar if their corresponding angles are congruent and their corresponding sides
are in proportion.

So letโs begin by looking at the
sides. The side ๐ต๐ถ in quadrilateral
๐ด๐ต๐ถ๐ท is corresponding to side ๐น๐บ in quadrilateral ๐ธ๐น๐บ๐ป. We can write the ratio of sides
๐ต๐ถ over ๐น๐บ as 28 over 14, which simplifies to two. If these quadrilaterals are
similar, then as we can see in the definition above, all the other corresponding
pairs of sides would have to be in this same proportion of two.

So letโs compare the sizes of
another pair of corresponding sides, for which we are given the lengths of. ๐ด๐ต is 31 centimeters and ๐ธ๐น is
23 centimeters. Writing these the same way round as
before, that is, with the side from ๐ด๐ต๐ถ๐ท as the numerator and the side on
๐ธ๐น๐บ๐ป as the denominator, we would put ๐ด๐ต over ๐ธ๐น, which gives us 31 over
23. But notice that this fraction
doesnโt simplify any further. And most importantly here, it is
definitely not equal to two. That means that the sides in
๐ด๐ต๐ถ๐ท and ๐ธ๐น๐บ๐ป are not in proportion. And therefore, we can answer the
question โAre the two polygons similar?โ as no.

When we are demonstrating that two
shapes are not similar, it is enough to show that a pair of sides are not in
proportion as we did here. Or we might demonstrate that a pair
of corresponding angles are not equal. However, as we can see in the
definition above, to prove two shapes are similar, we do need to prove that every
pair of corresponding angles are congruent and every pair of corresponding sides are
in proportion.