Drawing two altitudes of a triangle

a = {5, 0};
b = {0, 0};
c = {3, 6};
tri = {a, b, c};
TriangleConstruct[{a, b, c}, "Altitude"]
TriangleConstruct[{b, c, a}, "Altitude"]
TriangleConstruct[{c, a, b}, "Altitude"]

(* Line[{{0, 0}, {9/2, 3/2}}];
Line[{{3, 6}, {3, 0}}];
Line[{{5, 0}, {1, 2}}]
*)

So

a = {5, 0};
b = {0, 0};
c = {3, 6};
tri = {a, b, c};
alt = TriangleConstruct[tri, {"Altitude", All}];
Graphics[{Style[Triangle[tri], Opacity[0.2]], 
  TriangleConstruct[{a, b, c}, "Altitude"],
  TriangleConstruct[{b, c, a}, "Altitude"]}]