Triangle Sum Theorem [trahy-ang-guhl suhm theer-uhm]
Noun
This theorem clearly states that the sum of any triangle's (equilateral, isosceles, scalene, etc.) interior angles have to equal 180 degrees.
A nice two-column proof of this theorem is:
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Noun
This theorem clearly states that the sum of any triangle's (equilateral, isosceles, scalene, etc.) interior angles have to equal 180 degrees.
A nice two-column proof of this theorem is:
| Statements | Reasons |
Construct a line parallel to
 through point Y. Call this line  | Construction |
m 1 + m5 = mAYX | Angle Addition Postulate |
| mAYX + m4 = 180° | Linear Pair Postulate |
| m1 + m5 + m4 = 180° | Substitution |
 | Alternate Interior Angles Theorem |
m
2 = m4
m
3 = m5 | Definition of Congruence |
| m1 + m3 + m2 = 180° | Substitution |
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