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Rule

Interior Angles Theorem

The sum of the interior angles of a triangle is

Based on this diagram, the following relation holds true.

This theorem is also known as the Triangle Angle Sum Theorem.

Proof

Consider a triangle with vertices and and the parallel line to through Let and be the angles outside formed by this line and the sides and

triangle

By the Alternate Interior Angles Theorem, is congruent to and is congruent to

triangle

By the definition of congruent angles, and have the same measure. For the same reason, and also have the same measure. Furthermore, in the diagram it can be seen that and form a straight angle. Therefore, by the Angle Addition Postulate their measures add to By the Substitution Property of Equality, it follows that the sum of the measures of and is equal to Finally, in can be named

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