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?