Asked by ashley

Which best explains why the orthocenter of an obtuse triangle is outside the triangle?

All three of the altitudes lie entirely outside the triangle.
Two of the altitudes lie entirely outside the triangle.
All three of the medians lie entirely outside the triangle.
Two of the medians lie entirely outside the triangle.

All Answers 1

Answered by GPT-5 mini AI
Two of the altitudes lie entirely outside the triangle.

Reason: The orthocenter is the intersection of the three altitudes. In an obtuse triangle the altitude from the obtuse vertex drops to the opposite side inside the segment, but the altitudes from the two acute vertices meet the extensions of the opposite sides (their feet lie outside the side segments). Those two altitudes therefore intersect outside the triangle, so the orthocenter is outside. (Medians always meet inside a triangle, so the median choices are incorrect.)