This document discusses several theorems in plane geometry related to angles in triangles and parallel lines. It defines the sum of angles in a triangle theorem where the sum of the three interior angles equals 180 degrees. It also describes the opposite angle, supplementary angle, complimentary angle, exterior angle, and parallel lines theorems, relating corresponding, supplementary, complimentary, exterior, and alternate interior angles formed when lines intersect or are parallel.

1. Plane Geometry
M. Lula
SJAM 2013

2. Sum of Angles in a
Triangle, SATT
a
b c
a + b + c = 180o

3. Opposite Angle Theorem
x
y
x = y

4. Supplementary Angle
Theorem, SAT
x y
x + y = 18 0 o

5. Complimentary Angle
Theorem, CAT
x
y
x+ y = 9 0 o

6. Exterior Angle Theorem, EAT
a
b c
c = a + b

7. Parallel Lines, C-pattern
v
v
a
b
a + b = 180o

8. Parallel Lines, Z-pattern

9. Parallel Lines, F-Pattern