Question

lines c and d are cut by a transversal. identify four statements that prove line c is parallel to line d. ( mangle7 + mangle8 = 180^circ ) ( angle2congangle4 ) ( angle3congangle7 ) ( angle2congangle8 ) ( mangle2 + mangle5 = 180^circ ) ( mangle5 + mangle6 = 180^circ ) ( angle4congangle7 ) ( mangle1 + mangle5 = 180^circ ) ( angle4congangle6 ) ( angle3congangle8 )

Explanation:

Step1: Use the corresponding angles postulate

If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. $\angle3\cong\angle7$ (corresponding angles).

Step2: Use the alternate interior angles theorem

If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel. $\angle2\cong\angle8$ (alternate interior angles).

Step3: Use the same - side interior angles theorem

If two lines are cut by a transversal and the sum of the same - side interior angles is \(180^{\circ}\), the lines are parallel. \(m\angle2 + m\angle5=180^{\circ}\) (same - side interior angles).

Step4: Use the alternate exterior angles theorem

If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel. \(\angle4\cong\angle6\) (alternate exterior angles).

Answer:

\(\angle3\cong\angle7\), \(\angle2\cong\angle8\), \(m\angle2 + m\angle5 = 180^{\circ}\), \(\angle4\cong\angle6\)