Chapter 5 section 1

Today in class we learned about perpendiculars, medians, attitudes and bisectors

Perpendicular Bisectors Theorem-
An example of this theorem is shown in the picture above; it means that if for example segment CM is Perpendicular bisector of segment AB then that means that segments AC and BC are congruent to each other

Perpendicular Bisectors Theorem Converse-
Exactly the same as the perpendicular bisectors theorem except this is when you would know that segment AC and BC are congruent first. This converse would then prove that C is the perpendicular Bisector of segment AB.


Concurrent lines:
Three or more lines that intersect at the same point.

Point of Concurrency:
The point where the lines

INCENTER:
To find the incenter you must do as the picture shows below:

1.Bisect all the angles of the triangle
2.The point where the lines meet is where the incenter is
In this triangle with the incenter, since the angle was bisected meaning both sides are equal, this allows us to mark them congruent as shown in the picture above.

Incenter theorem- the incenter is equidistance from all sides



CIRCUMCENTER:
To find the circumcenter you must do as follows:

1.Find the midpoint of all three sides of the triangle
2.Draw a perpendicular line from the midpoint
3.The point where all three lines intercept is called the circumcenter
4.The sides where the midpoint is splitting the line are congruent as shown in the above picture

Circumcenter theorem- the circumcenter is equidistance from all three vertices




CENTROID:
To find the centroid you should:

1.Find the midpoint of all three sides of the triangle
2.Draw a line from the midpoint to the midpoint on the opposite side
3.The point where they intersect is called the centroid
4.The two sides of the midpoint are congruent to each other as shown below
Centroid Theorem: From the centroid to the side is half of the angle








ORTHOCENTER:
To find the orthocenter of a triangle you should do:

1. Make a perpendicular line from a side of the angle to the vertex across form it
2.Do this for all three sides
3.The point where the lines intercept is known as the orthocenter as shown in the picture below