RegionUnion gives the union of the regions
r1 = Region[Line[{{0, 0}, {1, 0}}]]; r2 = Region[Circle[{1, 1/2}, 1/2, {-π/2, π/2}]]; RegionUnion[r1, r2] 
From Mathematica 10 onwards there is a set of function for Derived Geometric Regions providing several ways of deriving new regions from existing ones, including combining them through Boolean operations and transforming them through a mapping.
RegionUnion gives the union of the regions
r1 = Region[Line[{{0, 0}, {1, 0}}]]; r2 = Region[Circle[{1, 1/2}, 1/2, {-π/2, π/2}]]; RegionUnion[r1, r2]
RegionUnion gives the union of the regions
r1 = Region[Line[{{0, 0}, {1, 0}}]]; r2 = Region[Circle[{1, 1/2}, 1/2, {-π/2, π/2}]]; RegionUnion[r1, r2]
From Mathematica 10 onwards there is a set of function for Derived Geometric Regions providing several ways of deriving new regions from existing ones, including combining them through Boolean operations and transforming them through a mapping.
RegionUnion gives the union of the regions
r1 = Region[Line[{{0, 0}, {1, 0}}]]; r2 = Region[Circle[{1, 1/2}, 1/2, {-π/2, π/2}]]; RegionUnion[r1, r2]