Video Transcript
The two quadrilaterals in the
given figure are congruent. Work out the perimeter of
๐ด๐ต๐ถ๐ท.
In this question, weโre not
given a congruency statement to help us work out the corresponding congruent
sides. But we can apply a little bit
of logic here. We can begin by noticing that
these shapes are a reflection of each other. We can see that angle ๐ด in our
quadrilateral ๐ด๐ต๐ถ๐ท would be congruent with angle ๐ธ in quadrilateral
๐ธ๐น๐บ๐ป. Angle ๐ต would be congruent
with angle ๐ป. Angle ๐ถ is congruent with
angle ๐บ. And angle ๐ท is congruent with
angle ๐น. We can, therefore, say that
๐ด๐ต๐ถ๐ท is congruent to ๐ธ๐ป๐บ๐น.
In order to work out the
perimeter of ๐ด๐ต๐ถ๐ท, we need to find some of the missing sides on this
quadrilateral. We could see that the side ๐ต๐ถ
would correspond with the side ๐บ๐ป, meaning that ๐ต๐ถ would also be 4.2. The last unknown side ๐ท๐ถ is
corresponding with side ๐น๐บ. So, it will be of length
three. Notice that as these two shapes
are congruent, this means that theyโll have the same perimeter. To find the perimeter of
๐ด๐ต๐ถ๐ท, we add up the lengths around the outside. So, we have 4.2 plus 4.1 plus
1.4 plus three, which is equal to 12.7. And we werenโt given any units
in the question. So, we donโt have any in the
answer.
