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GEOMETRY: Chapter 5

GEOMETRY: Chapter 5. 5.3: Medians and Altitudes. A median of a triangle is a segment from a vertex to the midpoint of the opposite side. The three medians of a triangle are concurrent. The point of concurrency, called the centroid , is inside the triangle.

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GEOMETRY: Chapter 5

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  1. GEOMETRY: Chapter 5 5.3: Medians and Altitudes

  2. A median of a triangle is a segment from a vertex to the midpoint of the opposite side. The three medians of a triangle are concurrent. The point of concurrency, called the centroid, is inside the triangle. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 319.

  3. Theorem 5.7:Concurrency of Medians of a Triangle The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 319.

  4. Ex. 1: In triangle HJK, P is the centroid and JP=12. Find PT and JT. Answer: 6,18 Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 320.

  5. Ex. 2: The vertices of triangle ABC are A(1,5), B(5,7), and C(9,3). • Which ordered pair give the coordinates of the centroid of triangle ABC? • (3,6) • (5,4) • (5,5) • (7,5) • Answer: C

  6. Altitudes: An altitude of a triangle is the perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side. Concurrency of Altitudes—the point at which the lines containing the three altitudes of a triangle intersect is called the orthocenter of the triangle. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 320.

  7. Theorem 5.8:Concurrency of Altitudes of a Triangle The lines containing the altitudes of a triangle are concurrent. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 320.

  8. Ex. 3: Show that the orthocenter can be inside, on, or outside the triangle.

  9. Ex. 3: Show that the orthocenter can be inside, on, or outside the triangle. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 320.

  10. Ex. 4: Prove that if an angle bisector of a triangle is also an altitude, then the triangle is isosceles. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 321.

  11. Write proof for Ex. 4 here:

  12. 5.3, p. 282, #3-10 all, 17-20 all.

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