Question Video: Understanding Properties of Congruence | Nagwa Question Video: Understanding Properties of Congruence | Nagwa

Question Video: Understanding Properties of Congruence Mathematics • First Year of Preparatory School

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The two quadrilaterals in the given figure are congruent. Work out the perimeter of π΄π΅πΆπ·.

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Video Transcript

The two quadrilaterals in the given figure are congruent. Work out the perimeter of π΄π΅πΆπ·.

In this question, weβ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 π΄ in our quadrilateral π΄π΅πΆπ· would be congruent with angle πΈ in quadrilateral πΈπΉπΊπ». Angle π΅ would be congruent with angle π». Angle πΆ is congruent with angle πΊ. And angle π· is congruent with angle πΉ. We can, therefore, say that π΄π΅πΆπ· is congruent to πΈπ»πΊπΉ.

In order to work out the perimeter of π΄π΅πΆπ·, we need to find some of the missing sides on this quadrilateral. We could see that the side π΅πΆ would correspond with the side πΊπ», meaning that π΅πΆ would also be 4.2. The last unknown side π·πΆ is corresponding with side πΉπΊ. So, it will be of length three. Notice that as these two shapes are congruent, this means that theyβll have the same perimeter. To find the perimeter of π΄π΅πΆπ·, 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 werenβt given any units in the question. So, we donβt have any in the answer.

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