Chapter Closure
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The two angles are corresponding angles. Since they are congruent, we know that TS and VU must be parallel lines by the Converse of the Corresponding Angles Theorem.
Note that this is insufficient information to claim that any sides are parallel. The only way TS and VU are parallel is if ∠ c and ∠ o are both 90^(∘). However, we do not have this information and, therefore, we cannot claim that the sides are parallel.
The two angles are alternate exterior angles. Since they are congruent, we know that TS and VU must be parallel lines by the Converse to the Alternate Exterior Angles Theorem.
Since ∠ m and ∠ o are corresponding angles and they are congruent, we know that ZY and XW are parallel.
Even though ∠ a is congruent to both ∠ m and ∠ o, we cannot claim that any other pair of lines are parallel.
Note that this is insufficient information to claim that any sides are parallel. Let's say that m∠ a=30^(∘). We can always move around XW and VU in multiple ways so that m∠ k equals 30^(∘) as well. Therefore, we cannot claim that any lines are parallel with this information.
Since ∠ k and ∠ c are congruent corresponding angles, we can claim that TS and VU are parallel by the Converse to the Corresponding Angles Theorem. Also, because ∠ c and ∠ f are congruent alternate interior angles, we can claim that ZY and XW are parallel by the Converse to the Alternate Interior Angles Theorem.
