Given: lines a and b are parallel and line c is a transversal. prove: 2 is supplementary to 8 what is the missing reason in the proof? statement reason 1. a || b, is a transv 1. given 2. ∠6 ≅ ∠2 2. ? 3. m∠6 = m∠2 3. def. of congruent 4. ∠6 is supp. to ∠8 4. def. of linear pair 5. ∠2 is supp. to ∠8 5. congruent supplements theorem corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem

The missing statement is Corresponding angles theorem

Step-by-step explanation:

In this question we are finding the reason for the statement ∠6 ≅ ∠2.

We will write the statements and then we'll give their reasons.

      Statement                                      Reason

1) a || b, is a transversal                             Given

2)   ∠6 ≅ ∠2                                         Corresponding angles theorem

3)  m∠6 = m∠2                                       def. of congruent

4) ∠6 is supp. to ∠8                                 def. of linear pair

5) ∠2 is supp. to ∠8                                congruent supplements theorem

Corresponding Angles Theorem states: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

The angles in matching corners are called Corresponding Angles.We can further define it as corresponding angles are angles that are in the same relative position at an intersection of a transversal and at least two lines. If the two lines are parallel then the corresponding angles are congruent

Thus the missing statement is Corresponding Angles Theorem.

step-by-step explanation:

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step-by-step explanation:

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