Quick Geometry..

[decibel]

If a line in a triangle is a median, does it cut the triangle into two congruent triangles?

[nolachrymose]

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!

[Gokul43201]

If it is isosceles, then yes, it does.

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.

[nolachrymose]

Whoops! You're right, Gokul. My mistake, blah. :blushing: