Final answer:
To determine which statements are true, we need to understand the concept of congruent angles and parallel lines. Statement a) is true because when two lines intersected by a transversal have corresponding angles that are congruent, the lines are parallel. Statement b) is false because congruent angles do not guarantee parallelism. Statement c) is false because the given congruent angles are not sufficient to determine parallelism. Statement d) is true because congruent angles imply parallel lines. Statement e) is false because the given congruent angles do not guarantee parallelism.
Step-by-step explanation:
In order to determine which statements are true, we need to understand the concept of congruent angles and parallel lines. When two lines are parallel, the corresponding angles are congruent. Using this concept, let's analyze each statement:
- a) p || q because <2 is congruent to <3. This statement is true because when two lines intersected by a transversal have corresponding angles that are congruent, the lines are parallel.
- b) p || q because <5 is congruent to <7. This statement is false because we cannot determine the parallelism of lines based on the congruence of angles 5 and 7. The congruence of angles does not guarantee parallelism.
- c) r || a because <2 is congruent to <4. This statement is false because the congruence of angles 2 and 4 does not provide enough information to determine the parallelism of lines r and a.
- d) r || s because <5 is congruent to <6. This statement is true because when angles 5 and 6 are congruent, it implies that lines r and s are parallel.
- e) r || s because <5 is congruent to <7. This statement is false because the congruence of angles 5 and 7 does not provide enough information to determine the parallelism of lines r and s.