Co-interior angles supplementary ⇒ parallel

Dependencies: Corresponding/alternate angles ⇔ lines parallel, Linear pair sums to 180°.

Statement

Let line $t$ cut lines $\ell_1$, $\ell_2$ at points $P_1$, $P_2$ ($P_1\neq P_2$). On a single side of $t$, the angle $\angle 1$ formed at $P_1$ by $t$ and $\ell_1$, together with the angle $\angle 2$ formed at $P_2$ by $t$ and $\ell_2$, is called a pair of co-interior angles — they lie between the two transversal lines, on the same side of $t$. The theorem asserts: