Question

Given: a and b are parallel and c is a transversal.
Prove: ∠2 ≅ ∠7

Parallel lines b and a are cut by transversal c. On line b where it intersects with line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 5, 6, 2. On line a where it intersects with line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 3, 7, 8, 4.
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
.

Answer 1

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 vertical angles are congruent. Angles 5 and 7 are congruent because corresponding angles (formed by parallel lines cut by a transversal) are congruent. Therefore, angles 2 and 7 are congruent based on the transitive property of congruence.