GeoGebra Classroom

# Chapter 4 Discovery

## Create triangle A, B, C below and label the vertices. Then use the applet to answer questions #1-5.

1. Record the measure of all three angles. Please record your answer as m<A = _____, m<B= ______, and m<C= _____.

2. Find the sum of the three angles. Record your answer here.

3. Drag one vertex of the triangle above. Does the measure of the individual angles change?

4. Drag one vertex of the triangle above. Does the sum of the three angles in the triangle change or remain the same? If it remains the same what is the sum?

5. The Angle Sum Theorem states: The sum of the measures of the angles in a triangle is ______. Please record this in your notes.

## Use the applet below to answer questions #6-8.

6. Measure angles A, B, and C inside the triangle above. Please record your answers as m<A= _____, m<B= _____, and m<C= _____.

7. <BAD and <BCE are called exterior angles of this triangle because the angle shares a vertex with a vertex of the triangle and one of the sides of the angle is one of the sides of the triangle. The other side of the angle is an extension of another side of the triangle. Please measure <BAD and <BCE above. Write your answer as m<BAD= _____ and m<BCE= _____.

If we are looking at the exterior angle <BAD, there are two remote interior angles in the triangle <B and <BCA. If we are looking at the exterior angle <BCE, there are two remote interior angles in the triangle <B and <BAC. There is a special relationship between the exterior angle in a triangle and the two remote interior angles.

8. Complete the Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to ______________. (You should be mentioning something about the remote interior angles.)