Question Video: Understanding Properties of Congruence Mathematics • 8th Grade

The two quadrilaterals in the given figure are congruent. Work out the perimeter of ๐ด๐ต๐ถ๐ท.

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Video Transcript

The two quadrilaterals in the given figure are congruent. Work out the perimeter of ๐ด๐ต๐ถ๐ท.

In this question, weโ€™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 ๐ด in our quadrilateral ๐ด๐ต๐ถ๐ท would be congruent with angle ๐ธ in quadrilateral ๐ธ๐น๐บ๐ป. Angle ๐ต would be congruent with angle ๐ป. Angle ๐ถ is congruent with angle ๐บ. And angle ๐ท is congruent with angle ๐น. We can, therefore, say that ๐ด๐ต๐ถ๐ท is congruent to ๐ธ๐ป๐บ๐น.

In order to work out the perimeter of ๐ด๐ต๐ถ๐ท, we need to find some of the missing sides on this quadrilateral. We could see that the side ๐ต๐ถ would correspond with the side ๐บ๐ป, meaning that ๐ต๐ถ would also be 4.2. The last unknown side ๐ท๐ถ is corresponding with side ๐น๐บ. So, it will be of length three. Notice that as these two shapes are congruent, this means that theyโ€™ll have the same perimeter. To find the perimeter of ๐ด๐ต๐ถ๐ท, 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 werenโ€™t given any units in the question. So, we donโ€™t have any in the answer.

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