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 they’re congruent or not.
So, if we start with our sides,
with side 𝐶𝐷 on our left quadrilateral, we can see from the one marking that
this is congruent with side length 𝑂𝑃 on our quadrilateral 𝑂𝑃𝑀𝑁. We can also see that the side
𝐹𝐸 on the quadrilateral 𝐶𝐷𝐸𝐹 is congruent with side 𝑀𝑁 on the
quadrilateral 𝑃𝑀𝑁𝑂. We can see that side 𝐶𝐹 is
congruent with side 𝑃𝑀 and side 𝐷𝐸 is congruent to side 𝑂𝑁. So, we’ve demonstrated that we
have four corresponding sets of congruent sides. However, this isn’t 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 aren’t the
same shape. So, we need to check the angles
in our polygons.
So, looking at angle 𝐶 in
quadrilateral 𝐶𝐷𝐸𝐹, we could say that this is congruent with angle 𝑀 in
quadrilateral 𝑃𝑀𝑁𝑂. Equally, angle 𝐷, which is
labelled as 104 degrees, would be congruent with angle 𝑁, which is also 104
degrees. We can see that angle 𝐸 of 76
degrees is congruent with angle 𝑂 of 76 degrees. And our final angle 𝐹 would be
congruent with angle 𝑃. So now, we’ve 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.
