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Chapter 5 Section 4 Medians and Altitudes

Chapter 5 Section 4 Medians and Altitudes. Objectives. Students will be able to identify properties of medians and altitudes in triangles. Essential Understanding. A triangle’s three medians are always concurrent The altitude of a triangle are concurrent. Median of a Triangle.

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Chapter 5 Section 4 Medians and Altitudes

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  1. Chapter 5 Section 4Medians and Altitudes

  2. Objectives Students will be able to identify properties of medians and altitudes in triangles

  3. Essential Understanding A triangle’s three medians are always concurrent The altitude of a triangle are concurrent

  4. Median of a Triangle Segment whose endpoints are a vertex and the midpoint of the opposite side

  5. Concurrency of Medians Theorem

  6. Centriod of the Triangle Point of Concurrency of the medians of a triangle Also called the center of gravity of a triangle This is the point where the triangle will balance Always inside the triangle Show on sketchpad

  7. Finding the Length of a Median ZA = 9, what is the length of ZC? What is the ration of ZA to AC? Explain.

  8. Altitude of a Triangle The perpendicular segment from the vertex of the triangle to the line containing the opposite side Can be on the inside, the outside, or a side of a triangle

  9. Concurrency of Altitudes Theorem The lines that contain the altitudes of a triangle are concurrent The point of concurrency is called the orthocenter sketchpad

  10. Finding the Orthocenter Find the equations of two altitudes Then solve the system of equations ΔDEF has vertices D(1, 2), E(1, 6), F(4, 2). What are the coordinates of the orthocenter of ΔDEF?

  11. Summary

  12. Homework Pg. 312 # 8 – 21, 24 – 27 18 problems

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