1. 5-3: Medians and Altitudes Medians and Altitudes in a Triangle
4/21/2017
5.3
Medians and Altitudes in a Triangle
M217 - Denna/Presta

2. 5-3: Medians and Altitudes
4/21/2017
Median
Segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side.
All three medians in a triangle intersect at the centroid of the triangle.
M217 - Denna/Presta

3. Length relationship within a Median
The centroid is located of the distance from each vertex to opposite midpoint

4. Ex: Find all segment lengthsP O

5. Ex: Find all segment lengthsP O

6. 5-3: Medians and Altitudes
4/21/2017
Altitude
Perpendicular segment from a vertex to the line containing the opposite side
All three altitudes in a triangle intersect at the orthocenter of the triangle.
M217 - Denna/Presta

7. 5-3: Medians and Altitudes
4/21/2017
Altitude (cont.)
Find the orthocenter
M217 - Denna/Presta

8. Finding the eqn of the line containing a median
Connects vertex to opposite midpoint
First find midpoint of opp side
Find slope between vertex point and midpoint
Write eqn with point-slope form

9. Ex: Find eqn of the line containing a median from A to BC
A (4, 6) B (-2, 8) C (0, 10)

10. Find the eqn of the line containing an altitude
Vertex to perp slope of opposite side
First find slope of opp side
Find the perp slope (opp reciprocal)
Write eqn with point-slope form using vertex and the perp slope

11. Ex: Find eqn of the line containing an altitude from A to BC
A (4, 6) B (-2, 8) C (0, 10)

12. Ex: Proof M A P B Statements Reasons 4-4: SAS, SSS 4/21/2017
M217 - Presta

13. What is the special name for each segment?RZ SV SU XY