  The unitarity triangles of the $3\times 3$ Cabibbo-Kobayashi-Maskawa (CKM)
matrix are studied in a systematic way. We show that the phases of the nine CKM
rephasing invariants are indeed the outer angles of the six unitarity triangles
and measurable in the $CP$-violating decay modes of $B_{d}$ and $B_{s}$ mesons.
An economical notation system is introduced for describing properties of the
unitarity triangles. To test unitarity of the CKM matrix we present some
approximate but useful relations among the sides and angles of the unitarity
triangles, which can be confronted with the accessible experiments of quark
mixing and $CP$ violation.
