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Could the median of a triangle be the perpendicular bisector?
Yes in equilateral triangle.
What triangle has an altitude which is also a median and angle bisector?
An isosceles or an equilateral triangle perhaps?
Can the median and altitude of a triangle meet in the same line segment?
Yes, if the triangle is isosceles or equilateral.
When is a median and an altitude the same segment?
In an isosceles or equilateral triangle, when from the vertex that is different from the others.
Does a median divide a triangle into two congruent triangles?
Yes * * * * * 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.
What ratio does a median divide two equilateral triangle?
A median divides any triangle in half.
Is the angle bisector also the median in an equilateral triangle?
No. The angle bisector is a line. Where the three lines meet is the median. In an equilateral triangle the INTERSECTION of the angle bisectors is the median.
Could the median of a triangle be the perpendicular bisector?
Yes in equilateral triangle.
If x be the length of a median of an equilateral triangle then its area is?
30
Can the median of an equilateral triangle be longer than its altitude?
For the equilateral triangle in Euclidean space(i.e, the triangles you see in general) median is the same as its altitude. So, both are of equal length.
What triangle has an altitude which is also a median and angle bisector?
An isosceles or an equilateral triangle perhaps?
Can the median and altitude of a triangle meet in the same line segment?
Yes, if the triangle is isosceles or equilateral.
When is a median and an altitude the same segment?
In an isosceles or equilateral triangle, when from the vertex that is different from the others.
Does a median divide a triangle into two congruent triangles?
Yes * * * * * 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.
Is it possible for an angle bisector to be the same line as a median?
Yes. In an isosceles or equilateral triangle, it always is.
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.
Do the medians of a triangle bisect the internal angles?
Not always. 1. The median to the base of an isosceles triangle bisects the vertex angle. 2. When the triangle is an equilateral triangle, then the medians bisect the interior angles of the triangle.
