Video: Understanding Properties of Congruence

The two quadrilaterals in the given figure are congruent. Work out the perimeter of 𝐴𝐡𝐢𝐷.

01:34

Video Transcript

The two quadrilaterals in the given figure are congruent. Work out the perimeter of 𝐴𝐡𝐢𝐷.

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 𝐴𝐡𝐢𝐷 would be congruent with angle 𝐸 in quadrilateral 𝐸𝐹𝐺𝐻. Angle 𝐡 would be congruent with angle 𝐻. Angle 𝐢 is congruent with angle 𝐺. And angle 𝐷 is congruent with angle 𝐹. We can, therefore, say that 𝐴𝐡𝐢𝐷 is congruent to 𝐸𝐻𝐺𝐹.

In order to work out the perimeter of 𝐴𝐡𝐢𝐷, we need to find some of the missing sides on this quadrilateral. We could see that the side 𝐡𝐢 would correspond with the side 𝐺𝐻, meaning that 𝐡𝐢 would also be 4.2. The last unknown side 𝐷𝐢 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 𝐴𝐡𝐢𝐷, 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.

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