Angles of Triangles Investigation

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

Answer each question IN COMPLETE SENTENCES in your notes.

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