Video Transcript
Consider two similar polygons π΄π΅πΆπ· and ππππΏ. Which angle in π΄π΅πΆπ· corresponds to angle π?
Letβs 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, π΄π΅πΆπ· and ππππΏ. And given they have four vertices, they must be two quadrilaterals. We donβt know what these polygons look like. So they could look like this or even like this. But it doesnβt 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 π΄ and read π΄π΅πΆπ·. So in the second shape, we start at the same corresponding vertex of π and read
ππππΏ. Vertices π΄ and π are corresponding, π΅ and π are corresponding, πΆ and π are
corresponding, and π· and πΏ are corresponding. And so the angles at each vertex also correspond.
We were asked which angle corresponds to angle π, which is in ππππΏ. So that would be angle π΅. Thus, we can give the answer that it is angle π΅. Although not required here, we can also use the similarity relationship to identify
corresponding sides in the same way. For example, side πΆπ· is corresponding to side ππΏ. 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.
