Compare your answers.

  1. List all of the pairs of angles for each relationship listed when each transversal, T1 and T2, crosses the parallel lines.
    2.  
    1. corresponding angles 

      The pairs of corresponding angles are ae, bf, cg, dh, im, jn, ko, and lp. Pairs like ai and bj are corresponding angles but they were not produced by a transversal crossing parallel lines.
    2. opposite angles 

      The pairs of opposite angles are ac, bd, eg, fh, ik, jl, mo, and np.
    3. alternate exterior 

      The pairs of alternate exterior angles are ag, bh, io, and jp. Pairs like bl and ci are alternate exterior angles, but they were not produced by a transversal crossing parallel lines.
    4. alternate interior

      The pairs of alternate interior angles are ce, df, km, and ln. Pairs like ak and dj are alternate interior angles but were not produced by a transversal crossing parallel lines.
     
  2. Based on everything you have seen so far, how do the sizes of the pairs of angles appear to compare for each relationship listed in 1?

    When a transversal crosses parallel lines, it appears that the pairs of angles for each of the relationships listed are the same size. This does not appear to be true when the lines are not parallel.

 

For further information on angle relationships see pp. 70–71 of Principles of Mathematics 11.

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