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Question Video: Understanding the Similarity between Polygons Mathematics

Consider two similar polygons 𝐴𝐡𝐢𝐷 and π‘‹π‘Œπ‘πΏ. Which angle in 𝐴𝐡𝐢𝐷 corresponds to βˆ π‘Œ?

02:23

Video Transcript

Consider two similar polygons 𝐴𝐡𝐢𝐷 and π‘‹π‘Œπ‘πΏ. Which angle in 𝐴𝐡𝐢𝐷 corresponds to angle π‘Œ?

Let’s begin by recalling that two polygons are similar if their corresponding angles are congruent and their corresponding sides are in proportion. So, we have two polygons here, 𝐴𝐡𝐢𝐷 and π‘‹π‘Œπ‘πΏ. And given they have four vertices, they must be two quadrilaterals. We don’t know what these polygons look like. So they could look like this or even like this. But it doesn’t matter what these quadrilaterals look like because we are given the similarity relationship. And the way in which this similarity relationship is written is very important.

We need to pay close attention to the order of the letters, which are the vertices. In the first shape, we start at vertex 𝐴 and read 𝐴𝐡𝐢𝐷. So in the second shape, we start at the same corresponding vertex of 𝑋 and read π‘‹π‘Œπ‘πΏ. Vertices 𝐴 and 𝑋 are corresponding, 𝐡 and π‘Œ are corresponding, 𝐢 and 𝑍 are corresponding, and 𝐷 and 𝐿 are corresponding. And so the angles at each vertex also correspond.

We were asked which angle corresponds to angle π‘Œ, which is in π‘‹π‘Œπ‘πΏ. So that would be angle 𝐡. Thus, we can give the answer that it is angle 𝐡. Although not required here, we can also use the similarity relationship to identify corresponding sides in the same way. For example, side 𝐢𝐷 is corresponding to side 𝑍𝐿. And it is also very important that if we are proving two polygons are similar, we should ensure that the similarity relationship that we write is given with the vertices of each shape in the correct corresponding order.

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