Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quick Geometry

  1. Sep 28, 2004 #1
    If a line in a triangle is a median, does it cut the triangle into two congruent triangles?
  2. jcsd
  3. Sep 28, 2004 #2
    Not necessarily, it depends on the type of triangle. If it is isosceles, then yes, it does. Otherwise, the median will simply divide the triangle into two congruent areas, but this does not imply that the triangles themselves are congruent. You can find more information at http://mathworld.wolfram.com/TriangleMedian.html.

    Hope that helps!
  4. Sep 28, 2004 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    This should be 'equilateral', not 'isosceles'.

    In an isosceles triangle, only one of the three medians divides the triangle into congruent parts. In an equilateral triangle, all three medians do this.
  5. Sep 29, 2004 #4
    Whoops! You're right, Gokul. My mistake, blah. :blushing:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook