Question

1. choose the correct answer.

which triangle illustrates an orthocenter?
d
a
b
c

Explanation:

To determine which triangle shows an orthocenter, we recall: The orthocenter of a triangle is the point where the three altitudes of the triangle intersect. An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

• Option A: The markings suggest it's a centroid (intersection of medians, where medians divide sides into halves), so not orthocenter.
• Option B: The markings (right angles on the sides, indicating perpendicular segments from vertices to opposite sides) show the intersection of altitudes. This matches the definition of an orthocenter.
• Option C: The right angles on the segments from the center to the sides suggest it's an incenter or something else, not altitudes from vertices.
• Option D: The markings suggest it's a circumcenter (equidistant from vertices, intersection of perpendicular bisectors), so not orthocenter.

Answer:

B. The triangle with right angles on the sides (altitudes) intersecting at point \( P \) (illustrating orthocenter)