Video Transcript
The two quadrilaterals in the
given figure are congruent. Work out the perimeter of
𝐴𝐵𝐶𝐷.
In this question, we’re 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 𝐴 in our
quadrilateral 𝐴𝐵𝐶𝐷 would be congruent with angle 𝐸 in quadrilateral
𝐸𝐹𝐺𝐻. Angle 𝐵 would be congruent
with angle 𝐻. Angle 𝐶 is congruent with
angle 𝐺. And angle 𝐷 is congruent with
angle 𝐹. We can, therefore, say that
𝐴𝐵𝐶𝐷 is congruent to 𝐸𝐻𝐺𝐹.
In order to work out the
perimeter of 𝐴𝐵𝐶𝐷, we need to find some of the missing sides on this
quadrilateral. We could see that the side 𝐵𝐶
would correspond with the side 𝐺𝐻, meaning that 𝐵𝐶 would also be 4.2. The last unknown side 𝐷𝐶 is
corresponding with side 𝐹𝐺. So, it will be of length
three. Notice that as these two shapes
are congruent, this means that they’ll have the same perimeter. To find the perimeter of
𝐴𝐵𝐶𝐷, 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 weren’t given any units
in the question. So, we don’t have any in the
answer.
