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Triangles: Medians, Altitudes & MidSegments

Explore the properties and relationships of medians, altitudes, and midsegments in triangles, including how they intersect and affect geometric calculations.

johncochran
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Triangles: Medians, Altitudes & MidSegments

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  1. Beyond CPCTC Lesson 3.4

  2. Medians: Every triangle has 3 medians A median is a line segment drawn from any vertex to the midpoint of its opposite side. A median bisects the segment.

  3. B E F A C D • Name the 3 medians of triangle ABC. • BD • CF • AE

  4. Altitudes: Every triangle has 3 altitudes. An altitude is a line segment drawn perpendicular from any vertex to its opposite side. *The altitude could be drawn outside the triangle to be perpendicular. Altitudes form right angles 90˚ You may need to use auxiliary lines (lines added)

  5. AD & BE are altitudes of ABC. AC & CD are altitudes of ABC. BD & AE are altitudes of ABC A D C B E

  6. Could an altitude also be a median? Yes, for an isosceles triangle when drawn from the vertex.

  7. MidSegments • A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle. • The midsegment is parallel to the third side and is half it’s length.

  8. Postulate: Two points determine a line, ray or segment. Determine (one and only one line)

  9. Given • An altitude of a forms rt. s with the side to which it is drawn. • Same as #2 • If s are rt. s, they are . • Reflexive Property. • Given • ASA (4, 5, 6) • CPCTC • Subtraction Property (6 from 8) • CD & BE are altitudes of ABC. • ADC is a rt. . • AEB is a rt. . • ADC  AEB • A  A • AD  AE • ADC  AEB • AB  AC • DB  EC

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