If \( AB \) is parallel to \( CD \), which statement must be true?

A. \( AB \) and \( CD \) do not intersect.

B. \( AB \) and \( CD \) intersect at 90° angles.

C. The perpendicular distance between \( AB \) and \( CD \) increases as the lines are traversed left to right.

D. The perpendicular distance between \( AB \) and \( CD \) decreases as the lines are traversed right to left.

AB and CD do not intersect.

Answered by olemakpadu | 2024-06-24

**Parallel lines **do not intersect and the **distance between **them is **constant. **The correct option is A.
How are parallel straight lines related?
**Parallel lines **have the same slope since the slope is like a measure of steepness and since **parallel lines **are of the same steepness , thus, are of the same slope.
Since the **given parallel **line has **equation **y = 2x + 2, thus its slope is 2 and thus, the **slope **of the **needed **line is 2 too.
If ab is **parallel **to cd then the **statement **that must be **true **is AB and CD do not intersect.
Hence, the correct option is A.

Learn more about Parallel lines:
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Answered by ap8997154 | 2024-06-24

The correct answer is A: A B and C D do not intersect. This is true because parallel lines, by definition, never meet. The remaining statements are false since they misrepresent the properties of parallel lines.
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Answered by olemakpadu | 2024-08-09