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6-1
The measure of an exteriorangle of a triangle is greater than the measure of either remoteinteriorangle.
6-2
If one side of a triangle is longer than a secondside, then the angleopposite the firstside is larger than the angleopposite the secondside.
6-3
If one angle of a triangle is larger than a secondangle, then the sideopposite the firstangle is longer than the side opposite the secondangle.
Corollaries
The perpendicularsegment from a point to a line is the shortestsegment from the point to the line.
The perpendicularsegment from a point to a plane is the shortestsegment from the point to the plane.
6-4
The sum of the lengths of any twosides of a triangle is greater than the length of the thirdside.
6-5
If twosides of onetriangle are congruent to twosides of anothertriangle, but the includedangle of the firsttriangle is larger than the includedangle of the second,then the thirdside of the firsttriangle is longer than the thirdside of the secondtriangle.
6-6
If twosides of onetriangle are congruent to twosides of anothertriangle, but the thirdside of the firsttriangle is longer than the thirdside of the second,then the includedangle of the firsttriangle is larger than the includedangle of the second.