Question

1. match each figure with the statement that proves (ellparallel m). (angle1congangle4) converse of the alternate exterior angles theorem (mangle3 + mangle5=180) converse of the corresponding angles theorem

Explanation:

Step1: Identify angle - type relationship for ∠1 and ∠4

∠1 and ∠4 are alternate exterior angles.

Step2: Recall angle - based parallel - line theorems

The converse of the Alternate Exterior Angles Theorem states that if alternate exterior angles are congruent, then the lines are parallel. Since ∠1≅∠4, the first figure uses the Converse of the Alternate Exterior Angles Theorem.

Step3: Identify angle - type relationship for ∠3 and ∠5

∠3 and ∠5 are corresponding angles.

Step4: Recall angle - based parallel - line theorems

The converse of the Corresponding Angles Theorem states that if corresponding angles are supplementary (i.e., their sum is 180°), then the lines are parallel. Since m∠3 + m∠5=180°, the second figure uses the Converse of the Corresponding Angles Theorem.

Answer:

For ∠1≅∠4: Converse of the Alternate Exterior Angles Theorem
For m∠3 + m∠5 = 180: Converse of the Corresponding Angles Theorem