Math CentralQuandaries & Queries


Question from Sophia, a student:

Does every triangle add up to 180 degrees? (Such as a unique triangle)

Hi Sophia,

In Euclidean Geometry the sum of the measures of the interior angles of a triangle is 180 degrees. This postulate is equivalent to the parallel postulate, for example look at this Wikipedia page. One proof begins with the diagram below where the line segment $PQ,$ through $A$ is parallel to $BC.$


Can you complete the proof?

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