Section 3.5 – The Triangle Sum Theorem

The Parallel Postulate

Given a line and a point not on the line, there is one and only one line that contains the given point and is parallel to the given line.

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The Triangle Sum Theorem

The sum of the measures of the angles of a triangle is 180°

Spheres

On the surface of a sphere, a line is defined as a great circle. A great circle divides a sphere into two congruent parts called hemispheres. (Equator)

There are no parallel lines on a sphere since they all intersect.

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the remote interior angles.

is an exterior angle. and 2 are remote interior angles.