Triangle Sum Exploration
Draw a Triangle, then measure all three angles of the triangle.
What is the sum of your angles?
Move your points around, then add them up again. Does the sum stay the same?
Write a conjecture (a statement based on evidence) about the angles in any triangle.
This is called the TRIANGLE SUM THEOREM
Test your conjecture by moving the points around in the diagram below.
Triangle Sum Theorem
Let's prove your conjecture. In the diagram below, follow these steps: 1. Create a line parallel to Line BC through Point A. (do this by clicking the "parallel line" tool, then clicking side BC then clicking point A). 2. Create a point on both sides of Point A. (do this by clicking the "point on object" tool, then clicking on the new line to the left of A, then click on the new line to the right of A). 3. Measure the 2 new created angles (Angle DAB and Angle CAE). 4. If any angles are congruent, color them the same color.
What kind of angles are Angle DAB and Angle ABC and what is their relationship?
What kind of angles are Angle CAE and Angle BCA and what is their relationship?
What kind of angles are Angle DAB, Angle BAC, and Angle CAE and what is their relationship?
Explain how this activity proves that the Triangle Sum Theorem