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altitudes

altitudes. bisectors. medians. SECTION 5-1 spi.3.2.J. Jim Smith JCHS. There are 3 of each of these special segments in a triangle. The 3 segments are concurrent. They intersect at the same point. This point is called the point of concurrency. The points have special names and

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altitudes

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  1. altitudes bisectors medians SECTION 5-1 spi.3.2.J Jim Smith JCHS

  2. There are 3 of each of these special segments in a triangle. The 3 segments are concurrent. They intersect at the same point. This point is called the point of concurrency. The points have special names and special properties.

  3. Altitudes Start at a vertex and form a 90° angle with the line containing the opposite side. Orthocenter

  4. The orthocenter can be located in the triangle, on the triangle or outside the triangle. Obtuse Right Legs are altitudes

  5. Angle Bisectors Angle bisectors start at a vertex and bisect the angle. Incenter

  6. Any point on an angle bisector is equidistance from the sides of the angle

  7. This makes the Incenter an equidistance from all 3 sides

  8. Perpendicular Bisectors A Perpendicular bisector of a side does not have to start at a vertex. It will form a 90° anglesand bisect the side. Circumcenter

  9. Any point on the perpendicular bisector of a segment is equidistance from the endpoints of the segment. AB is the perpendicular bisector of CD A C D B

  10. This makes the Circumcenter an equidistance from the 3 vertices

  11. Median The median starts at a vertex and ends at the midpoint of the opposite side. Centroid

  12. The centroid is 2/3’s of the distance from the vertex to the side. 32 10 2x 5 x X 16

  13. The centroid is the center of balance for the triangle. You can balance a triangle on the tip of your pencil if you place the tip on the centroid

  14. Quick notes Altitude .. Vertex .. 90° .. Orthocenter Angle Bisector.. Angle into 2 equal angles .. Incenter Perpendicular Bisector… 90° .. bisects side .. Circumcenter Median .. Vertex .. Midpoint of side ..Centroid

  15. Give the best name for AB A A A A A B B B B B | | | | | | MedianAltitudeNone Angle Perp Bisector Bisector

  16. Survival Training You’re Stranded On A Triangular Shaped Island. The Rescue Ship Can Only Dock On One Side Of The Island But You Don’t Know Which Side. At Which Point Of Concurrency Would You Set Up Camp So You Are An EqualDistance From All 3 Sides? INCENTER

  17. What If The Ship Could Only Dock At One Of The Vertices? Would You Change The Location Of Your Camp ? If So, Where? YES CIRCUMCENTER

  18. Where would you place a fire hydrant to make it equidistance to the houses and equidistance to the streets? ELM POST

  19. Angle bisector for the streets Perpendicular bisector for houses ELM POST

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