Question

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

Answer 1

Corresponding Angles Theorem: When parallel lines are crossed by a transversal lines then they form corresponding angles.

Explanation:

Let's visualize it to understand it better.

1 st Statement

1. a || b, c is a transv to both

Reason

given

2nd Statement

∠6 ≅ ∠2

Reason

Corresponding Angles Theorem: When parallel lines are crossed by a transversal lines then they form corresponding angles.

3rd Statement

m∠6 = m∠2

Reason

Definition of congruent: Two corresponding angles are congruent, i.e. have the same measure

4th Statement

∠6 is supp. to ∠8

Reason

Def. of linear pair: Two adjacent angles form a line, then they are supplementary angles and a linear pair.

5th Statement

∠2 is supp. to ∠8

Reason

Congruent supplements theorem. If ∠2 and ∠6 are corresponding and congruent and a linear pair, then ∠2 and ∠8 are supplementary.

Answer 2

The missing statement is Corresponding angles theorem

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.