# Angles of Triangles Investigation

- Author:
- Lydia Kenney

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*. 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?__*alternate interior angles*