1. 5-3: Medians and Altitudes (p. 10)

2. Apply properties of medians of a triangle. Apply properties of altitudes of a triangle. Objectives: 5-3: Medians and Altitudes

3. 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 ⅔ of the distance from each vertex to the midpoint of the opposite side. The centroid is always located inside the triangle. 5-3: Medians and Altitudes P A Z Y X C B 

4. Example 1: S is the centroid of LMN. RL = 21 and SQ =4. Find LS and NQ. LS = 14 Centroid Thm. Substitute 21 for RL. Simplify. 5-3: Medians and Altitudes

5. Centroid Thm. NS + SQ = NQ Seg. Add. Post. 12 = NQ Substitute 4 for SQ. Multiply both sides by 3. Substitute NQ for NS.Subtract from both sides.

6. 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

7. 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 The height of a triangle is the length of an altitude. Helpful Hint

8. Example 3: Find the orthocenter of ∆XYZ with vertices X(3, –2), Y(3, 6), and Z(7, 2). 5-3: Medians and Altitudes

9. Assignment: