In this investigation, we will discover and prove a relationship between the interior angles of a triangle.

1. Measure each interior angle of Triangle ABC. [br] Angle A = [br] Angle B = [br] Angle C = [br]2. Add the angles together. What is the sum?[br]3. Drag point B to make a different type of triangle. What is the sum of the 3 interior angles now?[br][br]Write this: [b]Conjecture: The sum of the three interior angles of a triangle is ____________. [br][br][/b][u]Now, we are going to PROVE your conjecture. [/u][br]4. Construct a line parallel to line AC through point B. [br]5. Put point D on the parallel line to the left of B. Put point E to the right of B. [br]6. Angle ABD, Angle B, and Angle CBE form a [b]straight line[/b]. What crucial information does that tell you?[br]Angle A and Angle ABD are [i][u]alternate interior angles[/u][/i]. What do you know about the measures of alternate interior angles?[br]7. Angle C and Angle CBE are also [u][i]alternate interior angles[/i][/u]. How are their measures related?[br]8. Measure Angles ABD and CBE to confirm your answers to #6 and #7. [br]9. How does this help you prove your conjecture?