To understand more about triangular geometry, we have to learn a few more terms.

## Midpoint

The Midpoint of a segment is the point that divides the segment into two congruent (identical) segments.

The mixpoint is:

\((x_m,y_m) = (\cfrac{x_2+x_1}{2}, \cfrac{y_2+y_1}{2}) \)

## Median

A Median is a line segment that extends from the vertex (corner) of one side of the triangle to the midpoint of the other side.

## Midsegment

A Midsegment is a line segment connecting the midpoints of two sides of a triangle. it is also parallel to the third side of the triangle and is half of the length of the third side!

## Altitude

An Altitude is a line segment that extends from the vertex (corner) of one side of the triangle and is perpendicular to the opposite line segment.

## Perpendicular Bisector

The Perpendicular Bisector is a line or a segment perpendicular to a segment that passes through the midpoint of the segment.
Then, the perpendicular bisector of a side of a triangle would be a line perpendicular to the side and passing through its midpoint.
Since there are three perpendicular bisectors on the sides of a triangle, and they meet in a single point,
that point would be called the circumcenter.
The three perpendicular bisector of the triangle would converge at the center of the red circle.

## Angle Bisector

The Angle bisector of an angle of a triangle would be a straight line that divides the angle into two congruent (equal) angles. Since there are three angle bisectors on the sides of a triangle, and they meet in a single point, that point would be called the **incenter**.

A line is drawn from a vertext of a triangle to the midpoint of the opposite side. The line is a _____.

Show Answer
The line is drawn from a vertex of a triangle to the midpoint of the opposide side. The line is a **median**. There is not enough information to determine if the
line is also an altitude or angle bisector.

What is the difference between a median and altitude?

Show Answer
Both median and altitudes are drawn from the vertex. However, a median is drawn to the **midpoint** of the opposite side where as an altitude is **perpendicular** to the opposite side.

Given two points (1,5) and (5,-5). What's the midpoint between these two point?

Show Answer
To find the midpoint of these two points, we have to add the coordinates of each axis and then divides them by two.

\( x_m = \cfrac{x_2+x_1}{2} = \cfrac{(1+5)}{2}=3\)

\( y_m = \cfrac{y_2+y_1}{2} = \cfrac{(5+-5)}{2}=0\)

The midpoint is at \((3,0)\)