Question

1 abc is a triangle 1 given 2 y || z 2 given 3 ∠1 ≅ ∠5, ∠3 ≅ ∠6 3? 4 m∠1 = m∠5, m∠3 = m∠6 4 def ≅ 5 m∠1 + m∠2 + m∠3 = m∠lam 5 ∠ addition postulate 6 m∠1 + m∠2 + m∠3 = 180° 6 def straight angle 7 m∠5 + m∠2 + m∠6 = 180° 7 substitution which could be the missing reason in step 3? alternate interior angles are congruent alternate exterior angles are congruent vertical angles are congruent corresponding angles are congruent

Explanation:

Since \(y\parallel z\) (given), and \(\angle1\) and \(\angle5\), \(\angle3\) and \(\angle6\) are pairs of angles formed by a transversal intersecting two parallel lines. Alternate interior angles are non - adjacent interior angles that lie on opposite sides of the transversal. When two parallel lines are cut by a transversal, alternate interior angles are congruent. So the reason for \(\angle1\cong\angle5,\angle3\cong\angle6\) is that alternate interior angles are congruent.

Answer:

alternate interior angles are congruent