MODULE IV VOCABULARY PART II

MODULE IV In continuing our discussion of triangles, it is important that we discuss concurrent lines and points of concurrence.

MODULE IV When three or more lines intersect at a common point, we call the lines concurrent lines. The point at which they meet is called the point of concurrence. In triangles, there are many points of concurrence.

MODULE IV There is one type of concurrent line that we have already discussed. The medians in any triangle are concurrent. The point at which they meet is called the the centroid. REMEMBER: The centroid is the center of gravity.

MODULE IV The centroid property states that the medians of a triangle intersect at a point called the centroid that is two thirds of the distance from each vertex to the midpoint of the opposite side.

MODULE IV The angle bisectors of a triangle are also concurrent lines. The point at which they meet is called the incenter.

MODULE IV The incenter property states that the angle bisectors of the sides of a triangle intersect at a point called the incenter that is equidistant from the sides of the triangle.

MODULE IV Using the incenter we can create what is called the incircle of our triangle. We simply place the spike of our compass on the incenter and the pencil on the intersection of the line and side of the triangle.

MODULE IV Lastly, we will discuss the perpendicular bisectors of the sides of a triangle. Take the time quickly to draw the perpendicular bisectors of the triangle below. What do you notice about them?

TRIANGLES CONTINUED The perpendicular bisectors of the sides of a triangle are concurrent lines! The point at which they meet is called the circumcenter.

TRIANGLES CONTINUED The circumcenter can inside, outside or directly on the triangle.

TRIANGLES CONTINUED The circumcenter property states that the perpendicular bisectors of the sides of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle.

MODULE IV Using this as the center I can create what is called the circumcircle. We simply place the spike of our compass on the circumcenter and the pencil on the vertex of the triangle.

MODULE IV We will have one more point of concurrence next time, but for now, this is a good start.