Question

5.3 medians and altitudes (ak)
altitude
a perpendicular segment
from a vertex of a triangle
to the line containing the
opposite side of the vertex
\\(\overline{ae}\\) is the altitude
perpendicular to \\(\overline{dc}\\)
triangle with vertices a, d, c and b as midpoint of ac; bd is median
median
a segment that has
endpoints at a vertex and the
midpoint of the side opposite
the vertex
\\(\overline{bd}\\) is the median that
bisects side \\(\overline{ac}\\)
concurrency of
medians
(theorem) -
the medians of a triangle
are concurrent at a point
that is two - thirds the
distance from each vertex
to the midpoint of the
opposite side
centroid
the point of concurrency
of the medians of a
triangle
triangle abc
measures
concurrency of
altitudes (theorem)
-
the lines that contain the
altitudes of a triangle are
concurrent.
orthocenter
the point of concurrency
of the altitudes of a
triangle
empty cell
empty cell
acute triangle
acute triangle with altitudes and orthocenter h
right triangle
right triangle xyz with altitude and orthocenter
obtuse triangle
obtuse triangle pqr with altitudes and orthocenter h

Explanation:

The content is about the concepts of medians and altitudes in triangles, including their definitions, concurrency theorems (for medians and altitudes), and how they appear in different types of triangles (acute, right, obtuse). This falls under the subfield of Geometry in Mathematics as it deals with the properties and relationships of geometric figures (triangles) and their components (medians, altitudes).

Answer:

The subfield is Geometry (under Mathematics).