Question

Determine the missing reason in the fifth line of the following proof.

Answer 1

Option D:

Converse of the corresponding angle postulate

Solution:

1. Given a || b.

2. Alternate Interior angle theorem:

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

⇒ ∠1 ≅ ∠3

3. Given ∠2 ≅ ∠3

4. Transitive property of equality:

If a = b and b = c, then a = c.

So, from (2) and (3), we can say ∠1 ≅ ∠2.

5. ∠1 and ∠2 are corresponding angles.

Converse of the corresponding angle postulate:

If two lines are cut by a transversal and the corresponding angles are equal then the two lines are parallel.

⇒ c || d.

Option D is the correct answer.

Converse of the corresponding angle postulate.