### Video Transcript

Are the polygons shown
congruent?

We can remind ourselves that
the word congruent means the same shape and size. A better mathematical
description is that polygons are congruent if all corresponding sides and
interior angles are congruent. If we want to check if these
two quadrilaterals are congruent, we need to check all the corresponding sides
and angles to see if theyβre congruent or not.

So, if we start with our sides,
with side πΆπ· on our left quadrilateral, we can see from the one marking that
this is congruent with side length ππ on our quadrilateral ππππ. We can also see that the side
πΉπΈ on the quadrilateral πΆπ·πΈπΉ is congruent with side ππ on the
quadrilateral ππππ. We can see that side πΆπΉ is
congruent with side ππ and side π·πΈ is congruent to side ππ. So, weβve demonstrated that we
have four corresponding sets of congruent sides. However, this isnβt sufficient
to show that two polygons are congruent. After all, we could, for
example, have a rectangle and a parallelogram which have congruent sides. But these clearly arenβt the
same shape. So, we need to check the angles
in our polygons.

So, looking at angle πΆ in
quadrilateral πΆπ·πΈπΉ, we could say that this is congruent with angle π in
quadrilateral ππππ. Equally, angle π·, which is
labelled as 104 degrees, would be congruent with angle π, which is also 104
degrees. We can see that angle πΈ of 76
degrees is congruent with angle π of 76 degrees. And our final angle πΉ would be
congruent with angle π. So now, weβve shown that we
also have four corresponding sets of congruent angles. This fits with our definition
of congruent polygons. So, yes, these polygons are
congruent.