Exterior Angle Theorem Proof
- Author:
- Kayla Moore
The exterior angle theorem states that if an exterior angle is created by extending a line from a triangle then the exterior angle created is greater than the two other interior angles of the triangle.
Proof: Let there exist a triangle ABC. Form an exterior angle by extending side AC by adding a point D. Create midpoint F on side BC by using Proposition 10. Draw a line BG so that BF FG by using a circle. Create a triangle by connecting C to G. By Proposition 4 we know that since AF FC and BF FG and AFB and CFG by Proposition 15, the bases of the triangles AB and CG are also equal and all the other angles are equal. From this we know that
BAC = FCG. By Proposition 14, we also know that BCA + ACG + GCD = 180. By Postulate 5, we know that: ABC + BCA + CAB = 180. Since ACF = ACG + GCD and BAC = FCG, we see that ACF is greater than BAC because Common Notion 5 tells us that the whole is greater than the part.