Given: triangle ABC. Prove: m<1 + m<2 + m<3 = 180
Translate ΔABC by vector AB to form straight <ABB' along the vector. The isometric properties of translation preserve _________, thus m<1 = m<B'BC'. Since <ABB' is a straight angle, we know that m<2 + m<CBC' + m<B'BC' = __________°. Translation also preserve ________, there for ensuring that line AC parallel to line BC'. Since line AC parallel to line BC', m<3 = m<CBC' because alternate ________ angles are congruent. By making two ________ into the straight angle relationship of m<2 + m<CBC' + m<B'BC' = 180º we arrive at the proof that m<1 + m<2 + m<3 = 180º.