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Yes
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No. A median is a line from a vertex to the midpoint of the opposite side. It divides the triangle into congruent parts only if
the triangle is equilateral
or
if the triangle is isosceles and it is the median from the unequal vertex.
In all other cases the two parts will not be congruent.
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If the median to a side of a triangle is also an altitude to that side then the triangle is isosceles How do you write this Proof?
Let the triangle be ABC and suppose the median AD is also an altitude.AD is a median, therefore BD = CDAD is an altitude, therefore angle ADB = angle ADC = 90 degreesThen, in triangles ABD and ACD,AD is common,angle ADB = angle ADCand BD = CDTherefore the two triangles are congruent (SAS).And therefore AB = AC, that is, the triangle is isosceles.
How is the altitude and a median of a triangle the same?
they are the same because the triangles side is equal
Which segment always divides a triangle into two triangles of equal areas?
median
How does the centroid divide each median in a triangle?
2/3 of the median is between the centroid and the vertex, 1/3 between the centroid and the side.
Can a median divide a triangle in equal area?
Sure. That's true of a median in every isosceles triangle, and every median in an equilateral triangle. In fact it is true for any median of any triangle. The two parts may not be the same shapes but they will have the same area. That is why the point where the three medians meet (centroid) is the centre of mass of a triangular lamina of uniform thickness.
