The sum of any two sides of a triangle is greater than the third side

1. Construct line AB.[br]2. Construct line AC.[br]3. Construct line BC. [br][br]Triangle ABC is a trilateral figure contained by three lines AB, BC, and AC by definition 19. [br][br]We want to show [br]i. AB+AC > BC[br]ii. AB+BC > AC[br]iii. BC+ AC > AB[br][br]4-5. Construct segment AD on line AB such that AD=AC. [br]6. Construct segment CD.[br][br]Triangle ACD is contained by lines AC, AD, and CD where AD=AC by construction.  [br]By definition 20, triangle ACD is isosceles. [br][br][br][br]