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1. If two parallel lines are cut by a transversal, then alternate interior angles are congruent

2. If two parallel lines are cut by a transversal, then corresponding angles are congruent

3. If two parallel lines are cut by a transversal, then alternate exterior angles are congruent

4. If two parallel lines are cut by a transversal, then complementary angles are congruent

1 If two parallel lines are cut by a transversal then alternate interior angles are congruent 2 If two parallel lines are cut by a

Answer :

Final answer:

In the context of parallel lines cut by a transversal, alternate interior angles, corresponding angles, and alternate exterior angles are congruent, but the statement on complementary angles is not always accurate. Such angles are not always congruent in that situation.

Explanation:

The subject under discussion pertains to the properties of parallel lines cut by a transversal in the realm of geometry. Here are the answers to the points:

  1. Yes, when two parallel lines are intercepted by a transversal, the alternate interior angles are indeed congruent. For instance, if we label them as angle 3 and 5, then angle 3 = angle 5.
  2. True, corresponding angles are equivalent when parallel lines are intersected by a transversal. An example would be angle 1 and angle 5, angle 1 = angle 5.
  3. It is correct to say that alternate exterior angles are congruent when a transversal cuts two parallel lines. Taking angle 1 and 7 as an instance, angle 1 = angle 7
  4. This statement is not quite accurate, complementary angles are not always congruent when two parallel lines are cut by a transversal. Complementary angles are two angles whose sum is 90 degrees, but this is not necessarily the case when considering lines intersected by a transversal.

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Rewritten by : Barada

When two parallel lines are cut by a transversal, the pairs of alternate interior angles, corresponding angles, and alternate exterior angles are congruent ,(1) ,(2) ,(3).

When two parallel lines are cut by a transversal, several angle relationships are formed:

  1. Alternate interior angles are congruent. For example, if angles a and b are alternate interior angles formed by a transversal cutting through parallel lines, then angle a is congruent to angle b.
  2. Corresponding angles are congruent. For example, if angles c and d are corresponding angles, then angle c is congruent to angle d.
  3. Alternate exterior angles are congruent. For example, if angles e and f are alternate exterior angles, then angle e is congruent to angle f.
  4. However, pairs of complementary angles are not necessarily congruent, as complementary angles are defined by their sum being 90 degrees, not by congruence.

Question-Two parallel lines are cut by a transversal, then which of the following are true?

1. Pair of alternate interior angles are congruent.

2. Pair Of corresponding angles are congruent.

3. Pair of alternate exterior angles are congruent.

4. Pair of complementary angles are congruent.