Question

If a transversal intersects two parallel lines, then which of the following alternatives is not true. 1 point a) Each pair of alternate interior angles is equal b) Each pair of corresponding angles is equal c) Each pair of co- interior angles is complementary d) Each pair of co- interior angles is supplementary

Answer 1

If a transversal intersects two parallel lines, each pair of alternate interior angles is equal, each pair of corresponding angles is equal, and each pair of co-interior angles is supplementary. The alternative that is NOT true is each pair of co-interior angles is complementary.

Step-by-step explanation:

If a transversal intersects two parallel lines, then the following statements are true:

1. Each pair of alternate interior angles is equal. Alternate interior angles are formed on opposite sides of the transversal and between the two parallel lines. For example, if two parallel lines are intersected by a transversal, angles 1 and 5 are alternate interior angles and they are congruent.
2. Each pair of corresponding angles is equal. Corresponding angles are formed on the same side of the transversal and in corresponding positions. For example, if two parallel lines are intersected by a transversal, angles 1 and 3 are corresponding angles and they are congruent.
3. Each pair of co-interior angles is supplementary. Co-interior angles are formed on the same side of the transversal and inside the two parallel lines. For example, if two parallel lines are intersected by a transversal, angles 3 and 6 are co-interior angles and they add up to 180 degrees.

Therefore, the alternative that is NOT true is option c) Each pair of co-interior angles is complementary (since they are actually supplementary).

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