$\overleftrightarrow{A B}$ is parallel to $\overleftrightarrow{D E}$

Alicia noticed that:
- $\angle w \cong \angle x$
- $\angle y \cong \angle x$

Note: Alicia used the following theorems:
- When a transversal crosses parallel lines, alternate interior angles are congruent.
- Vertical angles are congruent.

What theorem can Alicia prove using these congruent angles?
Choose 1 answer:
(A) When a transversal crosses parallel lines, corresponding angles are congruent.
(B) Angles that form a linear pair are complementary.
(c) When a transversal crosses parallel lines, same-side interior angles are congruent.
(D) When a transversal crosses parallel lines, alternate exterior angles are supplementary.

Question

$\overleftrightarrow{A B}$ is parallel to $\overleftrightarrow{D E}$

Alicia noticed that:
- $\angle w \cong \angle x$
- $\angle y \cong \angle x$

Note: Alicia used the following theorems:
- When a transversal crosses parallel lines, alternate interior angles are congruent.
- Vertical angles are congruent.

What theorem can Alicia prove using these congruent angles?
Choose 1 answer:
(A) When a transversal crosses parallel lines, corresponding angles are congruent.
(B) Angles that form a linear pair are complementary.
(c) When a transversal crosses parallel lines, same-side interior angles are congruent.
(D) When a transversal crosses parallel lines, alternate exterior angles are supplementary.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Given that $AB$ is parallel to $DE$ and a transversal cuts through them, we can use the properties of parallel lines and transversals to determine the relationship between angles $w$, $x$, and $y$. ‖ ‖ step 2 ⋮ Since angle $w$ is congruent to angle $x$ and angle $y$ is congruent to angle $x$, we can infer that angle $w$ is also congruent to angle $y$. ‖ ‖ step 3 ⋮ The congruence of angles $w$ and $y$ suggests that they are either corresponding angles or alternate interior angles, as those are the pairs of angles that can be congruent when a transversal crosses parallel lines. ‖ ‖ step 4 ⋮ The theorem that Alicia can prove using these congruent angles is that when a transversal crosses parallel lines, corresponding angles are congruent, because this is the only theorem that applies to non-adjacent angles on the same side of the transversal. ‖ ***A*** ∻Key Concept∻ ⚹Corresponding Angles Postulate⚹ ∻Explanation∻ ⚹When two parallel lines are cut by a transversal, the corresponding angles are congruent.⚹◊What is the relationship between alternate interior angles and congruent angles in geometry?⍭ Generate me a similar question◊

Sia