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
angles are congruent. angles 5 and
7 are congruent because
angles by
parallel lines cut by a transversal are congruent.
therefore, angles 2 and 7 are congruent based on the

Explanation:

• Vertical Angles: Vertical angles are formed when two lines intersect. They are opposite each other and have equal measures. In this case, \(\angle2\) and \(\angle5\) are vertical angles.
• Alternate Exterior Angles: Alternate exterior angles are formed when a transversal intersects two parallel lines. They are on the outside of the two parallel lines and on opposite sides of the transversal. Here, \(\angle5\) and \(\angle7\) are alternate exterior angles.
• Transitive Property: The transitive property of congruence states that if \(A\cong B\) and \(B\cong C\), then \(A\cong C\). Since \(\angle2\cong\angle5\) and \(\angle5\cong\angle7\), by the transitive property, \(\angle2\cong\angle7\).

Answer:

We can tell that angles \(2\) and \(5\) are congruent because vertical angles are congruent. Angles \(5\) and \(7\) are congruent because alternate exterior angles by parallel lines cut by a transversal are congruent. Therefore, angles \(2\) and \(7\) are congruent based on the transitive property.