This point lies inside a triangle if and only if all of its angles are acute. For 10 points each:
[10m] Name this point denoted “H” that is found at the intersection of the three altitudes of a triangle.
ANSWER: orthocenter
[10h] Along with the centroid and circumcenter, the orthocenter is used to define this construct. This construct is ill-defined for equilateral triangles because all three points coincide.
ANSWER: Euler line
[10e] The Euler line coincides with the line of symmetry in these triangles, which have exactly two sides with the same length.
ANSWER: isosceles triangles
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