Just as there are special names for special types of triangles, so there are special names for special line segments within triangles. Now isn't that kind of special?

## Base and altitude

Every triangle has three **bases** (any of its sides) and three **altitudes** (heights). Every altitude is the perpendicular segment from a vertex to its opposite side (or the extension of the opposite side) (Figure 1

**Figure 1 **

Altitudes can sometimes coincide with a side of the triangle or can sometimes meet an extended base outside the triangle. In Figure 2

*AC*is an altitude to base

*BC*, and

*BC*is an altitude to base

*AC*.

**Figure 2 **In a right triangle, each leg can serve as an altitude.

**
**

In Figure 3*AM* is the altitude to base *BC* .

**Figure 3**An altitude for an obtuse triangle.

It is interesting to note that in any triangle, the three lines containing the altitudes meet in one point (Figure 4

**Figure 4 **The three lines containing the altitudes intersect in a single point,

which may or may not be inside the triangle.

## Median

A **median** in a triangle is the line segment drawn from a vertex to the midpoint of its opposite side. Every triangle has three medians. In Figure 5*E* is the midpoint of *BC* . Therefore, *BE* = *EC*. *AE* is a median of Δ *ABC.*

**Figure 5**

In every triangle, the three medians meet in one point inside the triangle (Figure 6

**Figure 6**

## Angle bisector

An **angle bisector** in a triangle is a segment drawn from a vertex that bisects (cuts in half) that vertex angle. Every triangle has three angle bisectors. In Figure *ABC.*

**Figure 7**

In every triangle, the three angle bisectors meet in one point inside the triangle (Figure 8

**Figure 8**

**Figure 9**

**Example 1:** Based on the markings in Figure 10*QRS,* name a median of Δ *QRS,* and name an angle bisector of Δ *QRS*.

**Figure 10**

*QS* because *RT* ⊥ *QS* .

*SP* is a median to base *QR* because P is the midpoint of *QR* .

*QU* is an angle bisector of Δ *QRS* because it bisects ∠ *RQS.*