Altitude or median

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Deepthi Subbu: Master | Next Rank: 500 Posts; Posts: 298; Joined: Tue Feb 16, 2010 1:09 amFollowed by: 1 member; Thanked: 2 times

by Deepthi Subbu » Mon Aug 26, 2013 10:30 pm

Hi,

Will the median or altitude divide a triangle in to 2 congruent triangles?
Or median always divide triangles in to 2 equal halves whereas altitude does it only in case of right triangles inscribed in a circle?

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Source: Beat The GMAT — Problem Solving | Mon Aug 26, 2013 10:30 pm

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by [email protected] » Mon Aug 26, 2013 11:36 pm

Hi Deepthi,

You're asking about some very specific triangle concepts, but the GMAT very rarely uses these words (I've seen the word "altitude" sparingly; the only times that I've seen the word "median" were in reference to statistics questions, not geometry questions).

By definition, an altitude forms a 90 degree angle with the "base" of the triangle AND touches the highest "point" in the triangle. Sometimes an altitude is one of the sides, sometimes it's inside the triangle and sometimes it's outside of the triangle.

By definition, a median will run from a vertex of the triangle to the middle of the side opposite from it. The two pieces of the triangle will have the same area.

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