Question

Use the examples above to write a a paragraph proof proving the Triangle Sum Theorem. ( ask for example )

Answer 1

Given that line EC is parallel to line AB,

angle 1 = angle 4(because they are alternate angles. The lie in similar positions but on opposite sides of line AC

angle 3 = angle 5(because they are alternate angles. The lie in similar positions but on opposite sides of line BC

Also, angle 1, 2 and 3 are linear pairs. This means that

angle 1 + angle 2 + angle 3 = 180

Since angle 1 = angle 4 and angle 3 = angle 5, it means that

angle 4 + angle 2 + angle 5 = 180

Thus, the angle measures in the triangle add up to 180