Question

given: a and b are parallel and c is a transversal. prove: ∠2 ≅ ∠7 use the drop-down menus to complete the paragraph proof showing that alternate interior angles are congruent. we know that lines a and b are parallel and that line c is a transversal because that is given. we can tell that angles 2 and 5 are congruent because drop-down menu angles are congruent. angles 5 and drop-down menu cause drop-down menu angles by a transversal are congruent. and 7 are congruent based on the drop-down menu. the drop-down menu options are: vertical, corresponding, alternate interior, alternate exterior

Explanation:

Step1: Analyze ∠2 and ∠5

∠2 and ∠5 are vertical angles (opposite angles formed by intersecting lines). Vertical angles are congruent, so the first dropdown is "vertical".

Step2: Analyze ∠5 and ∠7

Since \(a \parallel b\) and \(c\) is a transversal, ∠5 and ∠7 are alternate interior angles. Alternate interior angles are congruent when lines are parallel, so the second dropdown is "alternate interior".

Step3: Transitive Property

If ∠2 ≅ ∠5 (vertical angles) and ∠5 ≅ ∠7 (alternate interior angles), then ∠2 ≅ ∠7 by the transitive property of congruence (the third dropdown would relate to this, but the key steps are identifying vertical and alternate interior angles).

Answer:

First dropdown: vertical
Second dropdown: alternate interior