Use the geometry tools to find the angle measures of [math]\angle[/math]ABD and [math]\angle[/math]DBC. Move points A and C around. What do you notice about the angle measures?
A segment or ray that cuts an angle into two equal parts.
If three or more lines intersect at a single point, then the lines are [b]concurrent lines[/b] The point where three or more lines intersect is called a [b]point of concurrency[/b]. The point of concurrency for the angle bisectors of a triangle is called the [b]incenter[/b].
What do you notice about the incenter D? Use the distance measuring feature to find the distance from point D to each vertex. Manipulate the triangle one more time. What do you notice?
Use the distance tool to find DE, DF, and DG. Move the vertices to make different triangles. What do you notice?
The Incenter of any triangle is [b]equidistant[/b] to the sides of the triangle.