transversal

A transversal is a line that passes through two lines in the same plane at two distinct points.

Angles of a Transversal across Parallel Lines

When the two lines crossed by the transversal are parallel, pairs of congruent and supplementary angles are formed, as named in subsections below.

\documentclass[tikz,margin=5pt]{standalone}
\usepackage{tkz-euclide}
%
\definecolor{color1}{HTML}{E93147}
\definecolor{color2}{HTML}{E0AC00}
\definecolor{color3}{HTML}{0BB94E}
\definecolor{color4}{HTML}{8A5CF5}
%
\begin{document}
\begin{tikzpicture}
    \node at (0,0) {};
    \node at (4,2) {};
    
    \tkzDefPoints{0/0.5/A, 0/1.5/B, 4/0.5/C, 4/1.5/D}
    \tkzDefPoints{1.5/0/Q, 2.5/2/R}    
    
    % \tkzDrawLines(A,C B,D Q,R)
    \tkzInterLL(A,C)(Q,R) \tkzGetPoint{M}
    \tkzInterLL(B,D)(Q,R) \tkzGetPoint{N}

    \tkzFillAngle[size=0.5, fill=color1](C,M,N)
    \tkzFillAngle[size=0.5, fill=color1](D,N,R)
    \tkzFillAngle[size=0.4, fill=color2](N,M,A)
    \tkzFillAngle[size=0.4, fill=color2](R,N,B)
    \tkzFillAngle[size=0.5, fill=color3](A,M,Q)
    \tkzFillAngle[size=0.5, fill=color3](B,N,M)
    \tkzFillAngle[size=0.4, fill=color4](Q,M,C)
    \tkzFillAngle[size=0.4, fill=color4](M,N,D)

    \begin{scope}[decoration={markings,
        mark=at position 0.85 with {\arrow{Stealth}},
        mark=at position 0.9 with {\arrow{Stealth}}
        },
        ]
        \tkzDrawLines[postaction={decorate}, very thick, latex-latex](A,C B,D)
    \end{scope}
    \tkzDrawLines[very thick, latex-latex](Q,R)
    
    % \tkzLabelPoints(A,B,C,D,Q,R,M,N)
\end{tikzpicture}
\end{document}

In total, 8 angles are formed, 4 of which are interior (between the two lines) and 4 of which are exterior (outside the two lines).

Alternate Angles

Alternate angles are the four pairs of angles that:

• have distinct vertex points,
• lie on opposite sides of the transversal, and
• both angles are interior or both angles are exterior.

Corresponding Angles

Corresponding angles are the four pairs of angles that:

• have distinct vertex points,
• lie on the same side of the transversal, and
• one angle is interior and the other is exterior.

Consecutive Interior Angles

Consecutive interior angles are the two pairs of angles that:

• have distinct vertex points,
• lie on the same side of the transversal, and
• are both interior.