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Answer:
11) C: (a, 4), (b, 3), (c, 2), (d, 1); V: (a, c), (b, d), (4, 2), (3, 1);
AI: (c, 4), (d, 3); AE: (a, 2), (b, 1); SI: (c, 3), (d, 4); SE: (a, 1), (b, 2)
12) : C: (a, y), (b, x), (c, w), (d, z); V:(a, c), (b, d), (w, y), (x, z);
AI: (b, z), (c, y); AE: (a, w), (d, x); SI: (b, y), (c, z); SE: (a, x), (d, w)
Explanation:
This is a vocabulary question. It is intended to see if you understand the meaning of the names given to the different angle pairs in this geometry.
All of the pairs of angles filling the first 4 blanks (corresponding, vertical, alt. int., alt. ext.) are congruent pairs of angles. The pairs of angles filling the last two blanks (same-side ...) are supplementary angles (total 180°).
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Corresponding angles lie in the same direction from the point of intersection. For example, the upper-left angles are corresponding.
Vertical angles are formed from opposite rays.
Alternate refers to angles on opposite sides of the transversal. (Same-side refers to angles on the same side of the transversal. Same-side angles are also called consecutive angles.)
Interior refers to angles that are between the parallel lines. Exterior refers to angles outside the parallel lines.
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The figures are a bit fuzzy. We assume the angle designations are (CW around the intersection point from upper left, left group first) ...
Figure 11) {a, b, c, d}, {4, 3, 2, 1}
Figure 12) {d, c, b, a}, {z, w, x, y}
If this is not correct, you will need to make appropriate substitutions in the pairs given below.
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11) Corresponding: (a, 4), (b, 3), (c, 2), (d, 1)
Vertical: (a, c), (b, d), (4, 2), (3, 1)
Alternate Interior: (c, 4), (d, 3)
Alternate Exterior: (a, 2), (b, 1)
Same-side Interior: (c, 3), (d, 4)
Same-side Exterior: (a, 1), (b, 2)
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12) Corresponding: (a, y), (b, x), (c, w), (d, z)
Vertical: (a, c), (b, d), (w, y), (x, z)
Alternate Interior: (b, z), (c, y)
Alternate Exterior: (a, w), (d, x)
Same-side Interior: (b, y), (c, z)
Same-side Exterior: (a, x), (d, w)
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Additional comment
The vocabulary is used to cite various theorems supporting claims regarding angle relationships. In practice, when the lines are parallel, all obtuse angles related to a transversal are congruent, all acute angles are congruent, and the acute angles are supplementary to the obtuse angles. (If the angles are 90°, neither acute nor obtuse, then they are all congruent.)