Given: Lines a and b are parallel and line c is a transversal. Prove: Angle2 is supplementary to Angle8 Horizontal and parallel lines a and b are cut by transversal c. On line a where it intersects line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line b where it intersects line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7. 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

This theorem states that, when the two parallel lines are intersected by the same transversal then the corresponding angles formed at the intersection of the two lines are congruent.

When a line intersects two parallel lines then the angle formed at the same relative position at each intersections are known as corresponding angles to each other.

Given: a and b are parallel lines and c is the transversal.

Also, transversal c cuts two horizontal parallel lines a and b.

Now, four angles are formed due to intersection at line a, they are:

∠1, ∠2, ∠4 and ∠3. (As shown in the figure)

Similarly, four angles are formed at line b due to the intersection of c:

∠5, ∠6, ∠8 and ∠7. (As shown in the figure)

Now, we have to prove: ∠2 is supplementary to ∠8.

Here is the proof:

a || b and c is the transversal. (given)

From the figure we can see that ∠2 and ∠6 are corresponding angles, hence by corresponding angles theorem we can state that:

∠6 ≅ ∠2

Now, by using the definition of congruent, we can write:

m∠6 = m∠2

From the figure we can see that ∠6 and ∠8 are the linear pair of angles hence, ∠6 is supplementary to ∠8.

Now since we obtained that, ∠6 = ∠2, we can write:

∠2 is supplementary to ∠8.

Hence proved that, ∠2 is supplementary to ∠8.

Therefore, the missing reason of the statement ∠6 ≅ ∠2 is:

Corresponding Angles Theorem

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