Geometry Session 1 HW Last Question

GRE Quant Problem Solving
1

I have been having trouble understanding why Triangle STU has the height of TV for this problem?

To me the Base would be TU, the Height is TV and the Hypotenuse is SU. The other way to look at it could be Base is ST, Height is TU, but Hypotenuse is still SU. In a sense to me, SU is always a Hypotenuse and never a Base of the triangle.

I’ve noticed some external sites tried explaining it through perpendicularity but I was not aware of that potential rule. Some have said SU would be the base, but as I see it that would only be the case for Triangle SVT.

Is there a way you could dumb it down for me to better understand this problem as I have been stuck on it. If you could draw/outline it out to make it clear, that would be greatly appreciated!

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2

Every triangle has a base and a height, but it need not have a hypotenuse. I would not look for a hypotenuse if it’s irrelevant, as is the case here. Also, the base and the altitude (height) must be perpendicular, and TU is not perpendicular to TV.

The height can be inside the triangle. Heights are defined for all triangles. I think you are assuming that the triangle must be a right triangle for a height to exist.

The height of a triangle is a line segment drawn from a vertex, perpendicular to the line or side opposite the vertex.