Welcome to a lesson on constructing an
angle bisector using Geometer’s Sketchpad. Let’s first construct an angle. Remember an angle is formed by two rays having the same initial point. So the clicker on this tool here, the third option is to construct a ray. So we’ll select this tool, click to form the
initial point, and drag to another point on the ray, let’s say here. Now we can position the mouse over the initial point again and then click and dragged to form the second ray. Now we’ll go ahead and click on the selection tool, then click on the white area to unselect the two rays. Normally what we do with the compass is we sing an arc that intersects both sides of the angle. But in Geometer’s Sketchpad we’ll construct a circle with the center of the vertex of the angle that intersects the the two sides. So now we’ll select the circle tool. Click and hold on the vertex, and then drag to construct the circle. So maybe something like this. Now let’s go ahead and right click on this and change the color to green, so it stands out a little bit. Now we’ll determine the intersection points of the circle and the two sides of the angle. So with the circle already selected we’ll click on the selection tool, and then click on one of the rays. Notice the circle and one ray are selected. And then we’ll select construction, intersection. And notice how it found that point of intersection. Now let’s go ahead and unselect everything by clicking in the white. Select the circle and the other ray and do the same. Construct and then intersection. Let’s click in the white again. Now using a compass and straightedge we would swing arc with the point of the compass at these two intersection points. But in Geometer’s Sketchpad we want to construct two congruent circles with one center at this intersection point, and the other center at this intersection point. And the only restriction is we have to make the circles large enough so the two circles would intersect. Let’s go ahead and click on the circle tool. Let’s go to this point of intersection, click and drag to form one of the circles, maybe here. And I’m going to go ahead and right click, change it to thin, and also change the color so it looks a little bit different. I’ll go ahead and change it to red. Now the other circle that we make at this center must be congruent to this red circle. So let’s go ahead and measure the radius of this circle. We’ll click on measure and then radius. Now let’s go ahead and click on the selection tool. With this radius already selected, we’ll click on the other intersection point of the circle and the other side of the angle. So with these two selected we’ll go ahead and select construct, and then circle by centre plus radius. And notice how it constructed a congruent circle to the other red circle. Now let’s go ahead and select the other circle so that both circles are selected, and then we want to find the intersection points of these two circles. So construct, intersections. Let’s go ahead and unselect everything by clicking in the white. And now we can go ahead and construct the angle bisector passing through the vertex and these two points of intersection. So we’ll go ahead select the vertex and then just one of the other points of intersection, let’s say this one. Well go up to construct and then ray. Now again let’s go ahead right click on this. Let’s go ahead and change the color to this light blue. And let’s also make it thick. So right click and thick. Let’s go ahead and unselect everything by clicking in the white. And just to verify that we do have the angle bisect, let’s go ahead and measure the two angles to make sure they are congruent. To do that we just need to select three points. One point on one side of the angle, the
vertex. And then one point on the other side maybe this point here. Select measure and then angle. Unselect everything click on the white. And now we’ll measure the lower angle, so we’ll select this point, the vertex, and say this point. And we’ll go ahead and measure this angle as well. Notice how they are congruent angles and if we try to change the angle, we can see that the blue ray remains the angle bisector of the larger angle. And that’s it for this video. I hope you found it helpful.