Question

communicate your answer

1. when two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent?

Explanation:

Step1: Recall corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are congruent. For example, if we have two parallel lines \(l_1\parallel l_2\) and a transversal \(t\), then \(\angle1\) and \(\angle5\) (in the standard angle - numbering for parallel - line - transversal configuration) are corresponding angles and \(\angle1\cong\angle5\).

Step2: Recall alternate interior angles

Alternate interior angles are also congruent. If \(l_1\parallel l_2\) and \(t\) is the transversal, then \(\angle3\) and \(\angle6\) are alternate interior angles and \(\angle3\cong\angle6\).

Step3: Recall alternate exterior angles

Alternate exterior angles are congruent. For \(l_1\parallel l_2\) and transversal \(t\), \(\angle1\) and \(\angle8\) are alternate exterior angles and \(\angle1\cong\angle8\).

Step4: Recall vertical angles

Vertical angles (formed by the intersection of two lines) are always congruent. When the transversal intersects one of the parallel lines (or itself), vertical angles are formed. For example, if two lines intersect at a point, \(\angle a\) and \(\angle b\) are vertical angles, then \(\angle a\cong\angle b\).

Answer:

Corresponding angles, alternate interior angles, alternate exterior angles, and vertical angles.