Question

18 $overrightarrow{ab}$ is parallel to $overrightarrow{cd}$ and perpendicular to both $overrightarrow{ef}$ and $overrightarrow{gh}$. which statements are true? select two correct answers. a $overrightarrow{cd}$ is parallel to $overrightarrow{gh}$. b $overrightarrow{ab}$ is parallel to $overrightarrow{gh}$. c $overrightarrow{ef}$ is parallel to $overrightarrow{gh}$. d $overrightarrow{ef}$ is perpendicular to $overrightarrow{cd}$. e $overrightarrow{ef}$ is perpendicular to $overrightarrow{gh}$.

Explanation:

Step1: Recall parallel - perpendicular relationships

Given $\overrightarrow{AB}\parallel\overrightarrow{CD}$ and $\overrightarrow{AB}\perp\overrightarrow{EF}$, $\overrightarrow{AB}\perp\overrightarrow{GH}$.

Step2: Analyze option A

There is no information suggesting $\overrightarrow{CD}$ is parallel to $\overrightarrow{GH}$, so A is false.

Step3: Analyze option B

We know $\overrightarrow{AB}\perp\overrightarrow{GH}$, not parallel, so B is false.

Step4: Analyze option C

There is no information suggesting $\overrightarrow{EF}$ is parallel to $\overrightarrow{GH}$, so C is false.

Step5: Analyze option D

Since $\overrightarrow{AB}\parallel\overrightarrow{CD}$ and $\overrightarrow{AB}\perp\overrightarrow{EF}$, then $\overrightarrow{EF}\perp\overrightarrow{CD}$ (if a line is perpendicular to one of two parallel lines, it is perpendicular to the other).

Step6: Analyze option E

There is no information suggesting $\overrightarrow{EF}$ is perpendicular to $\overrightarrow{GH}$, so E is false.

Answer:

D. $\overrightarrow{EF}$ is perpendicular to $\overrightarrow{CD}$