Question

in this figure, transversal ( e ) intersects lines ( a ), ( b ), ( c ), and ( d ). which must be true? ( aparallel c ) ( bparallel c ) ( bparallel d ) ( aparallel d )

Explanation:

Step1: Recall parallel - line angle relationships

When two parallel lines are intersected by a transversal, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary.

Step2: Analyze the given angles

For lines \(a\) and \(c\), the angles formed by the transversal are \(70^{\circ}\) and \(70^{\circ}\). These are corresponding angles. If corresponding angles are equal, then the two lines are parallel.

Step3: Check other pairs

For \(b\) and \(c\), the angles \(120^{\circ}\) and \(70^{\circ}\) do not satisfy any parallel - line angle relationships. For \(b\) and \(d\), the angles \(120^{\circ}\) and \(130^{\circ}\) do not satisfy any parallel - line angle relationships. For \(a\) and \(d\), the angles \(70^{\circ}\) and \(130^{\circ}\) do not satisfy any parallel - line angle relationships.

Answer:

\(a\parallel c\)