Welcome to our new unit about Special Lines and Points that show up in Triangles! Our first lesson is about [b]perpendicular bisectors[/b] and [b]circumcenters[/b]. Let's start by writing our first standard at the top of your notes for today. [b]LT5.1 - I can use properties of perpendicular bisectors and circumcenters in triangles.[/b] 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. [b]Perpendicular Bisector -[/b] 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. [b]Theorem 5.1: Perpendicular Bisector Theorem - [/b]If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoint of the segment. [b]Theorem 5.2: Converse of Perpendicular Bisector Theorem - [/b]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 [b]circumcenters[/b] 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. [b]Theorem 5.3: Circumcenter Theorem- [/b] 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 [b]circumcenter[/b] 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..