## 3.3: The Angle Addition Postulate

Now that we have learned how to find a midpoint of a line segment using Geometry Sketchpadlet's investigate bisecting an angle with Geometry Sketchpad

Step by Step Instructions

a. Like the construction in the book we start by constructing an angle

b. Since we are not using a compass, we will select a point on one of the sides of the angle such that if we construct a circle with radius equal to the distance from the vertex of our angle and the new point on our angle, the circle will intersect both sides of our angle. (Draw point on one side of angle, then highlight vertex and new point. Select "Circle by Center & Point" from the "Construction" menu)

c. Now identify the point where the circle intercepts the other side of the angle

d. Since we want to just focus on the angle let's hide the circle. (Highlight the circle, from the "Display" menu select "Hide Circle")

e. To draw the arc in the interior of the angle we will construct circles from the new points on the angles. Construct 2 circles with the centers being the new points on the angle and the point on the circles being the vertex of the angle. (Highlight new point on top segment then highlight vertex, from the "Construct" menu select "Circle by Center + Point"; do the same with the new point and vertex on the bottom segment)

f. Now locate the point where the two circles intercept in the interior of the angle. Then hide the circles.

g. Construct a segment from the point in the interior to the vertex of our angle, this is our angle bisector. (Highlight point in interior and vertex, from the "Construction" menu select "Segment")

If we had a protractor we could measure the two angles to see if they were equal, but since we don't let's again use the "Measure" menu to verify our construction

h. Highlight the endpoint of our original angle, the vertex, and the point in the interior from the "Measure" menu select "Angle" do the same highlighting the other endpoint of our original angle, the vertex, and the point in the interior.

Thus we have verified that our construction is accurate.