Question

What is another way to summarize the outcome of this proof?

1
Given: AB II CD
A
B
4
6
5
Prove: 23 a 26
с
7
8
D
Statement
Reason
1. AB||CD
1. Given
2.23 27
2. Corresponding angles theorem
3. Vertical angles are congruent
3. 27 - 26
4. m23 = m27
m27 = m_6
5. m23 = m26
4. Definition of congruence
5. Substitution
6.23 - 26
6. Definition of congruence
Vertical angles are congruent.
B. If two lines are parallel, then alternate interior angles are
congruent.
C. Corresponding angles theorem.
D. If two lines are parallel, then alternate exterior angles are
congruent.

Answer 1

Option B: If two lines are parallel, then alternate interior angles are

congruent.

Explanation:

Notice that angles 3 and 6 are INTERNAL relative to the parallel lines, that is located in between the parallel lines. They are also alternate angles. Therefore, the correct answer is:

"If two lines are parallel, then alternate interior angles are congruent."