Consider two similar polygons 𝐴𝐵𝐶𝐷 and 𝑋𝑌𝑍𝐿. Which angle in 𝐴𝐵𝐶𝐷 corresponds to angle 𝑌?
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, 𝐴𝐵𝐶𝐷 and 𝑋𝑌𝑍𝐿. 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 𝐴𝐵𝐶𝐷. So in the second shape, we start at the same corresponding vertex of 𝑋 and read
𝑋𝑌𝑍𝐿. Vertices 𝐴 and 𝑋 are corresponding, 𝐵 and 𝑌 are corresponding, 𝐶 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 𝑌, which is in 𝑋𝑌𝑍𝐿. So that would be angle 𝐵. Thus, we can give the answer that it is angle 𝐵. Although not required here, we can also use the similarity relationship to identify
corresponding sides in the same way. For example, side 𝐶𝐷 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.