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Geometry

Geometry. Section 5.4 – Medians and Altitudes. Primary Vocabulary Terms in Ch. 5 (Review). Midsegment Connects two midpoints Midsegment parallel to third side and half length of third side Perpendicular Bisector Perpendicular to segment and goes through midpoint of segment

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Geometry

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  1. Geometry Section 5.4 – Medians and Altitudes

  2. Primary Vocabulary Terms in Ch. 5(Review) • Midsegment • Connects two midpoints • Midsegment parallel to third side and half length of third side • Perpendicular Bisector • Perpendicular to segment and goes through midpoint of segment • All points on it are equidistant from endpoints of segment • Angle Bisector • Cuts angle into two congruent pieces • All points on it are equidistant from sides of angle • Distance from point to side must be perpendicular to the side

  3. Primary Vocabulary Terms in Ch. 5(New) • Median (Section 5.4) • Connects vertex to opposite midpoint • If all three medians are drawn, they are concurrent and meet at a point called the centroid

  4. Primary Vocabulary Terms in Ch. 5(New) • Median (Section 5.4) • Connects vertex to opposite midpoint • If all three medians are drawn, they are concurrent and meet at a point called the centroid • The centroid is the center of mass of a triangle

  5. Primary Vocabulary Terms in Ch. 5(New) • Median (Section 5.4) • Theorem 5.8 – Median Concurrency: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 • The distance from the centroid to the midpoint is half the distance from the centroid to the vertex

  6. Practice Problems MP, KW, and RG are medians a. b. If RG = 24 then GA = c. If AW = 3, then KA = d. If MA = 8, then PA =

  7. Primary Vocabulary Terms in Ch. 5(New) • Altitude (Section 5.4) • Goes from vertex to be perpendicular to the opposite side • Note that sometimes this means you must extend the opposite side for it to be perpendicular • Primarily used as the “height” of a triangle when finding area

  8. Primary Vocabulary Terms in Ch. 5(New) • Altitude (Section 5.4) • Theorem 5.9 – Altitude Concurrency:Altitudes of a triangle meet at a point called the Orthocenter • Orthocenter does not have any other special properties that we will discuss

  9. Primary Vocabulary Terms in Ch. 5(New) • Altitude (Section 5.4) • Determine the area of the two triangles

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