Question

for numbers 11 - 14, are $overrightarrow{ac}$ and $overrightarrow{df}$ parallel? explain your reasoning. 11.) 12.) 13.) 14.)

Explanation:

Step1: Recall parallel - line criteria

If corresponding angles are equal, alternate - interior angles are equal, or same - side interior angles are supplementary, then the lines are parallel.

Step2: Analyze problem 11

The angle adjacent to the $57^{\circ}$ angle is $180 - 57=123^{\circ}$. This $123^{\circ}$ angle and the $123^{\circ}$ angle given are corresponding angles. Since corresponding angles are equal, $\overrightarrow{AC}$ and $\overrightarrow{DF}$ are parallel.

Step3: Analyze problem 12

The $62^{\circ}$ angles are corresponding angles. Since corresponding angles are equal, $\overrightarrow{AC}$ and $\overrightarrow{DF}$ are parallel.

Step4: Analyze problem 13

The $143^{\circ}$ angle and the $37^{\circ}$ angle are supplementary ($143 + 37=180^{\circ}$). These are same - side interior angles. Since same - side interior angles are supplementary, $\overrightarrow{AC}$ and $\overrightarrow{DF}$ are parallel.

Step5: Analyze problem 14

The $65^{\circ}$ angles are corresponding angles. Since corresponding angles are equal, $\overrightarrow{AC}$ and $\overrightarrow{DF}$ are parallel.

Answer:

1. Yes, because corresponding angles are equal.
2. Yes, because corresponding angles are equal.
3. Yes, because same - side interior angles are supplementary.
4. Yes, because corresponding angles are equal.