Question

problem 14: (first taught in lesson 27) using this diagram, select the pair of lines that must be parallel if ∠4≅∠7. if there are no lines that have to be parallel, select “none.” after you pick your answer press go. a. k || j b. d || e c. k || i d. d || f e. none

Explanation:

Step1: Recall parallel - line postulates

When two lines are cut by a transversal, for lines to be parallel, certain angle - relationships must hold.

Step2: Analyze given angle relationship

\(\angle4\) and \(\angle7\) are not corresponding angles, alternate interior angles, or alternate exterior angles with respect to any of the pairs of lines \(k\parallel j\), \(d\parallel e\), \(k\parallel i\), or \(d\parallel f\) formed by the transversals in the diagram. So, if \(\angle4\cong\angle7\), no pair of lines in the given options must be parallel.

Answer:

E. None