Video Transcript
The two quadrilaterals in the
given figure are congruent. Work out the perimeter of
π΄π΅πΆπ·.
In this question, weβre 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 π΄ in our
quadrilateral π΄π΅πΆπ· would be congruent with angle πΈ in quadrilateral
πΈπΉπΊπ». Angle π΅ would be congruent
with angle π». Angle πΆ is congruent with
angle πΊ. And angle π· is congruent with
angle πΉ. We can, therefore, say that
π΄π΅πΆπ· is congruent to πΈπ»πΊπΉ.
In order to work out the
perimeter of π΄π΅πΆπ·, we need to find some of the missing sides on this
quadrilateral. We could see that the side π΅πΆ
would correspond with the side πΊπ», meaning that π΅πΆ would also be 4.2. The last unknown side π·πΆ is
corresponding with side πΉπΊ. So, it will be of length
three. Notice that as these two shapes
are congruent, this means that theyβll have the same perimeter. To find the perimeter of
π΄π΅πΆπ·, 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 werenβt given any units
in the question. So, we donβt have any in the
answer.
