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5.3

5.3. Medians and Altitudes in a Triangle. 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. Length relationship within a Median. M. P. I.

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5.3

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  1. 5.3 Medians and Altitudes in a Triangle

  2. 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 centroidof the triangle.

  3. Length relationship within a Median M P I • The centroid is located of the distance from each vertex to opposite midpoint O L S E

  4. Ex: Find all segment lengths M P I O L S E

  5. Ex: Find all segment lengths M P I O L S E

  6. 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.

  7. Altitude (cont.) • Find the orthocenter

  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. M Ex: Proof A P B

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

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