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Medians and altitudes

Medians and altitudes. Section 5.4. Medians of a triangle. A median of a triangle is a segment from a vertex to the midpoint of the opposite side. Altitudes of a triangle.

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Medians and altitudes

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  1. Medians and altitudes Section 5.4

  2. Medians of a triangle • A median of a triangle is a segment from a vertex to the midpoint of the • opposite side.

  3. Altitudes of a triangle • 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.

  4. Concurrency • The point of intersection of the lines, rays, or segments is called the point of concurrency.

  5. Points of concurrency • The point of concurrency of the three medians of a triangle is called the centroid. • The point of concurrency of the three altitudes of a triangle is called the orthocenter. • The centroid will always be inside the triangle. The orthocenter can be inside, on, or outside the triangle.

  6. What is special about the Centroid? • 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.

  7. What is special about the Orthocenter? • There is nothing special about the point of concurrency of the altitudes of a triangle.

  8. In RST, Qis the centroid and SQ = 8. Find QWand SW. SQ = SW 2 2 3 3 8= SW 2 3 Multiply each side by the reciprocal, . 12= SW 12 –8 = 4. SW – SQ = Then QW = EXAMPLE 1 Use the centroid of a triangle SOLUTION Concurrency of Medians of a Triangle Theorem Substitute 8 for SQ. So, QW = 4 and SW = 12.

  9. Assignment • p. 322: 3-7, 17-22

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