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5-3 Medians and Altitudes

(p. 10)

5-3 Medians and Altitudes

Objectives

- Apply properties of medians of a triangle.
- Apply properties of altitudes of a triangle.

5-3 Medians and Altitudes

- Medians of triangles
- Endpoints are a vertex
- and midpoint of opposite side.
- Intersect at a point called the centroid
- Its coordinates are the average of the 3

vertices. - The centroid is ? of the distance from each

vertex to the midpoint of the opposite side. - The centroid is always located inside the

triangle.

P

5-3 Medians and Altitudes

Example 1

S is the centroid of ?LMN. RL 21 and SQ 4.

Find LS and NQ.

Centroid Thm.

Substitute 21 for RL.

LS 14

Simplify.

Centroid Thm.

NS SQ NQ

Seg. Add. Post.

Substitute 4 for SQ.

Multiply both sides by 3.

12 NQ

5-3 Medians and Altitudes

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?

5-3 Medians and Altitudes

- Altitudes of a triangle
- A perpendicular segment from a vertex to the line

containing the opposite side. - Intersect at a point called the orthocenter.
- An altitude can be inside, outside, or on the

triangle.

5-3 Medians and Altitudes

Example 3

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

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

5-3 Medians and Altitudes

Assignment

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