Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
3. Proofs with Parallel Lines
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Exercise 22 Page 515

Yes
Explanation: See solution.

Practice makes perfect

We can determine if AC and DF are parallel lines by, for example, examining consecutive interior angles. According to the Consecutive Interior Angles Converse, we know that two lines cut by a transversal are parallel if a pair of consecutive interior angles are supplementary.

Identifying consecutive interior angles

The figure does not provide a pair of consecutive interior angles, but if we determine ∠ ABE, we can compare it with 37^(∘) which is its consecutive interior angle. Note that ∠ ABE and 143^(∘) are vertical angles. Therefore, we can, by the Vertical Angles Congruence Theorem, know that they are congruent m∠ ABE=143^(∘) As we already established, consecutive interior angles are supplementary if the lines cut by the transversal are parallel. Therefore, m∠ ABE and 37^(∘) should add up to 180^(∘) if AC and DF are parallel
37^(∘)+m∠ ABE=180^(∘)
37^(∘)+ 143^(∘)? =180^(∘)
180^(∘)=180^(∘)
Since ∠ ABE and 37^(∘) are supplementary, we know that AC and DF are parallel.