Decide whether the statement is always, sometimes, or never true.

In a scalene triangle, the altitude and the angle bisector from a given vertex are different line segments.

Question

Decide whether the statement is always, sometimes, or never true.

In a scalene triangle, the altitude and the angle bisector from a given vertex are different line segments.

anonymous · Answer

That would be always true.

Suppose they *were* the same line segment.  Then the two new triangles formed would be congruent by ASA (the 90-degree from the altitude, the altitude line segment, and the bisected angle).  This would mean that the two sides that form the given vertex angle would be equal...which would mean you'd have an isosceles rather than a scalene.  This is a contradiction so our assumtion that they are the same line segment must be wrong.

Therefore they are *always* different line segments.
Q.E.D.