Welcome to our new unit about Special Lines and Points that show up in Triangles! Our first lesson is about perpendicular bisectors and circumcenters. Let's start by writing our first standard at the top of your notes for today. LT5.1 - I can use properties of perpendicular bisectors and circumcenters in triangles. First, let's make sure we all understand the actual definition of Perpendicular Bisectors. You can record it in the vocabulary section on the last page of your packet. Perpendicular Bisector - a line or segment that is perpendicular to a given segment and goes through its midpoint (cuts it in half). We have two theorems relating to perpendicular bisectors that we need to copy into our packets. Theorem 5.1: Perpendicular Bisector Theorem - If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoint of the segment. Theorem 5.2: Converse of Perpendicular Bisector Theorem - If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
Now that we understand what circumcenters are, let's add one more theorem into our packet of understanding. Copy the diagram above into the third column of your packet for this theorem. Theorem 5.3: Circumcenter Theorem- The perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle. Be sure to also add the circumcenter to the vocabulary section on the last page of your packet: It is the point of concurrency (where all the lines intersect together) of the three perpendicular bisectors of the three sides of a triangle. You can move ahead to the next page in the workbook (2 - Circumcenter Worksheet) to explore a little more about circumcenters. Make sure to consider the questions at the bottom of the page before working through the practice to check your understanding..