Question

Which of the following is the reason for statement #7 in the table above?​ The choices are,

A) Converse of the alternate interior angles theorem
B) Converse of the corresponding angles theorem
C) Converse of the same side consecutive angles theorem
D) transitive property

Answer 1

C) Converse of the same side consecutive angles theorem.

Explanation:

Answer 2

The reason for statement #7.

C) Converse of the same side consecutive angles theorem.

Explanation:

For Parallel Lines:

Same side consecutive angles theorem

When the lines are parallel, the interior angles on the same side of the transversal are supplementary.

Here,

It is Converse Of above Statement

∠ 6 and ∠ 13 are supplementary

i.e

∠ 6 + ∠ 13 = 180°

Therefore the Reason is

C) Converse of the same side consecutive angles theorem.

That is If ∠ 6 and ∠ 13 are supplementary then the Lines are Parallel

i.e t₁ || t₂