Sum of Exterior Angles of a Triangle
Constructing the Exterior Angles of a triangle
1. On the open Geogebra window below, use the segment tool[icon]/images/ggb/toolbar/mode_segment.png[/icon] to construct a non-regular triangle.[br]2. Label the vertices A, B and C using the text tool. [icon]/images/ggb/toolbar/mode_text.png[/icon][br]3. Construct one set of exterior angles using the ray tool[icon]/images/ggb/toolbar/mode_ray.png[/icon]. Make sure your exterior angles all go the same way, like the picture below. Label the exterior parts of the angles D (next to A), E (next to B) and F (by C).
Construct the triangle and exterior angles below.
4. Measure angles DAB, EBC and FCA [icon]/images/ggb/toolbar/mode_angle.png[/icon]. Select either the two lines that make the angle or 3 vertices to measure the angle. Make sure to measure the exterior angles less than 180.
5. Add your 3 angles together.
What is the sum of the 3 exterior angles?
6. Drag your vertices around and allow the angles to change. Add them again.
What is the sum of the exterior angles now?
Complete the following conjecture: The sum of the exterior angles of a triangle is ___________