Question 472244: is the vertical line down the middle of a scalene triangle perpendicular to the base
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if the base is horizontal, then any vertical line drawn to intersect with it would be perpendicular to that base.
if you are drawing the altitude to any triangle, then, by definition, that line drawn from the vertex of an angle to intersect with the opposite side of the triangle must be perpendicular to the opposite side.
if the triangle has an obtuse angle (greater than 90 degrees), then drawing the altitude can be a little tricky, because you would have to extend the base in order for the angle opposite that base to be perpendicular to it.
The following diagrams might help you understand.
Just keep in mind, that, by definition, the altitude to a triangle is perpendicular to the base, with the base being the side opposite the angle you are drawing the altitude from.
in the triangle on the top left, the angle is A and the base is BC and the altitude to the triangle is AD.
in the triangle on the top right, the angle is B and the base is AC and the altitude to the triangle is BD.
in the triangle on the bottom, the angle is A and the base is BC and the extension to the base is BD and the altitude to the triangle is AD.
while the altitude is dropped to the extension of the base, the triangle is still only ABC and does not include BD. The extension is usually drawn with a dashed line to indicate it is not part of the triangle.
vertical and perpendicular don't necessarily mean the same thing. a vertical line is only perpendicular to another line if that other line is horizontal.
the altitude to a triangle is always perpendicular to the base of the triangle, but not necessarily vertical. it depends on whether the base is horizontal or not. calling it vertical to the base forces the base to be horizontal. calling it perpendicular to the base allows the base to be any orientation.
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