Which is a correct two column proof?

Option a is the correct answer.

Solution:

Option a:

Step 1: Given

line l and m are parallel lines.

Step 2: ∠p and ∠d are vertically opposite angles.

Vertical angle theorem:

If two angles are vertically opposite then the two angles are congruent.

∠p ≅ ∠d by vertical angle theorem.

Step 3: ∠d and ∠c are same side interior angles.

we know that, interior angles in the same side are supplementary.

So, ∠d and ∠c are supplementary.

Step 4: ∠c and ∠k are vertically opposite angles.

∠c ≅ ∠k by vertical angle theorem.

Step 5: By step 2 and step 3,

∠p and ∠c are supplementary.

Substitute step 4, we get

∠p and ∠k are supplementary.

Hence it is true.

Option b:

Step 1: Given

line l and m are parallel lines.

Step 2: ∠p ≅ ∠k by corresponding angles is given.

∠p and ∠h are the corresponding angles.

∠p and ∠k are not corresponding angles.

From step 2 on wards it is not true. so need not to verify the other steps.

Hence it is false.