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Medians and Altitudes of Triangles

5-3

Section 5.3

Holt Geometry

Holt McDougal Geometry

- Warm Up
- What is the name of the point where
- The perpendicular bisectors meet?
- The angle bisectors meet?
- 2. Find the midpoint of the segment with the

given endpoints. - (1, 6) and (3, 0)
- 3. Write an equation of the line containing the

points (3, 1) and (2, 10) in point-slope form.

A median of a triangle is a segment whose

endpoints are a vertex of the triangle and the

midpoint of the opposite side.

Every triangle has three medians, and the medians

are concurrent.

The point of concurrency of the medians of a

triangle is the centroid of the triangle . The

centroid is always inside the triangle. The

centroid is also called the center of gravity

because it is the point where a triangular region

will balance.

Example 1A Using the Centroid to Find Segment

Lengths

In ?LMN, RL 21 and SQ 4. 1. Find LS. 2.

Find NQ.

In ?JKL, ZW 7, and LX 8.1. 1. Find KW. 2.

Find LZ.

Example 2 Problem-Solving Application

A sculptor is shaping a triangular piece of iron

that will balance on the point of a cone. At what

coordinates will the triangular region balance?

What are the coordinates of the centroid of the

triangle below?

An altitude of a triangle is a perpendicular

segment from a vertex to the line containing the

opposite side. Every triangle has three

altitudes. An altitude can be inside, outside, or

on the triangle. The point of concurrency is

called the orthocenter.

(No Transcript)

Find the orthocenter of ?XYZ with vertices X(3,

2), Y(3, 6), and Z(7, 1).

Lesson Quiz

In ?ABC, AE 12, DG 7, and BG 9. Find each

length. 1. AG 2. GC 3. GF

For Items 4 and 5, use ?MNP with vertices M (4,

2), N (6, 2) , and P (2, 10). Find the

coordinates of each point. 4. the

centroid 5. the orthocenter

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