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 are formed when two lines intersect. They are opposite each other and have equal measures. So, \(\angle2\) and \(\angle5\) are vertical angles.
• Alternate exterior angles are a pair of angles that lie outside the two parallel lines and on opposite sides of the transversal. For parallel lines \(a\) and \(b\) cut by transversal \(c\), \(\angle5\) and \(\angle7\) are alternate exterior angles.
• The transitive property of congruence states that if \(A\cong B\) and \(B\cong C\), then \(A\cong C\). Here, since \(\angle2\cong\angle5\) and \(\angle5\cong\angle7\), by transitive property \(\angle2\cong\angle7\).

Answer:

First blank: vertical; Second blank: alternate exterior; Third blank: transitive property of congruence.