Question

given ( overline{ef}paralleloverline{gh} ) and ( overline{ab}paralleloverline{cd} ).
prove ( angle gjicongangle lkf ).

Explanation:

Step1: Corresponding angles

Since \(EF\parallel GH\), \(\angle BIK\cong\angle GJI\) (corresponding angles).

Step2: Alternate exterior angles

Since \(AB\parallel CD\), \(\angle BIK\cong\angle LKF\) (alternate exterior angles).

Step3: Transitive property

By the transitive property of congruence, \(\angle GJI\cong\angle LKF\).

Answer:

\(\angle GJI\cong\angle LKF\) is proved.