Question

determine if l || m based on the information given on the diagram. if yes, state the converse that proves the lines are parallel.

Explanation:

Step1: Recall parallel - line postulates

If two lines are cut by a transversal, then the lines are parallel if corresponding angles are congruent, alternate - interior angles are congruent, or same - side interior angles are supplementary.

Step2: Analyze problem 1

The two given angles ($65^{\circ}$ and $115^{\circ}$) are same - side interior angles. Since $65^{\circ}+115^{\circ}=180^{\circ}$, by the converse of the same - side interior angles postulate, $l\parallel m$.

Step3: Analyze problem 2

The two given angles ($128^{\circ}$ and $52^{\circ}$) are same - side interior angles. Since $128^{\circ}+52^{\circ}=180^{\circ}$, by the converse of the same - side interior angles postulate, the lines are parallel.

Step4: Analyze problem 3

The right - angle markings indicate that the corresponding angles are congruent (both are right angles or $90^{\circ}$). By the converse of the corresponding angles postulate, the lines are parallel.

Step5: Analyze problem 4

There is not enough information given about the angles formed by the transversal and the lines to determine if the lines are parallel. There are no congruent corresponding, alternate - interior, or supplementary same - side interior angles shown.

Answer:

1. Yes, by the converse of the same - side interior angles postulate.
2. Yes, by the converse of the same - side interior angles postulate.
3. Yes, by the converse of the corresponding angles postulate.
4. No.