3.1.1 Planes, Lines, and Angles (continued)
Example 2 Classifying Pairs of Angles In the figure given below, line p is a transversal since it is a line that intersects two coplanar lines, lines m and n , at two different points. Eight angles are formed by the intersections of lines p , m and n . These angles are numbered 1 through 8. Pairs of these angles are classified in this example as either corresponding angles, alternative interior angles, alternate exterior angles, or same-side interior angles.
Notice that ∠ 3 and ∠ 5 lie on opposite sides of the transversal, p . They are also in the space between the two other lines, m and n, so ∠ 3 and ∠ 5 are in the interior of m and n . Therefore, ∠ 3 and ∠ 5 are alternate interior angles. ∠ 4 and ∠ 5 lie on the same side of the transversal, p .They are also in the interior of m and n . Therefore, ∠ 4 and ∠ 5 are same-side interior angles. Notice that ∠ 2 and ∠ 6 are in the same relative position within each group of four angles. In other words, these angles lie on the same side of p and on the same side of m and n ( ∠ 2 is above m and ∠ 6 is above n ). Therefore, ∠ 2 and ∠ 6 are corresponding angles. Another pair of corresponding angles is ∠ 4 and ∠ 8. ∠ 1 and ∠ 7 lie on opposite sides of the transversal, p , and outside the other two lines, m and n , so ∠ 1 and ∠ 7 are said to be in the exterior of lines m and n . So, ∠ 1 and ∠ 7 are alternate exterior angles.
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