Exercises 11-16, use the diagram. (See Example t B S A E C D What is another name for \overline{BD}?
The Correct Answer and Explanation is:
To answer this question, let’s first interpret what it means:
Question:
Exercises 11–16, use the diagram. (See Example)
t B S A E C D
What is another name for $\overline{BD}$?
Since you mentioned “t B S A E C D”, we can assume this is a straight line or a figure showing points placed in a certain order. Let’s interpret that as a line with points in this order from left to right:
t — B — S — A — E — C — D
✅ Correct Answer:
Another name for $\overline{BD}$ is $\overline{tD}$ or $\overline{Dt}$, as long as t, B, and D all lie on the same straight line and B is between t and D.
However, more precisely, a correct and concise alternative name for $\overline{BD}$ is $\overline{DB}$, since a line segment can be named by its two endpoints in any order.
📘 Explanation
In geometry, line segments are portions of a line that have two distinct endpoints. The notation $\overline{BD}$ refers to the line segment with endpoints B and D. This segment includes all the points between B and D, including B and D themselves.
A line segment can be named by any two points on it, specifically by its endpoints. Importantly, the order of the letters doesn’t matter for a segment—$\overline{BD}$ and $\overline{DB}$ represent the same segment.
If the diagram shows points arranged on a line such as:
t — B — S — A — E — C — D,
then all these points lie on the same straight line. This means that any pair of points along that path can form a line segment, such as $\overline{BS}$, $\overline{AE}$, or $\overline{BD}$.
Therefore, since points B and D lie on the same line, and the segment between them is $\overline{BD}$, any name that uses these two endpoints (in any order) is correct. For example:
- $\overline{BD}$
- $\overline{DB}$
If the question is asking for another name for $\overline{BD}$, then the natural and accurate answer is:
$\overline{DB}$
In summary, naming a line segment depends on its endpoints, and since the order of letters doesn’t affect the segment’s identity, $\overline{DB}$ is another correct name for $\overline{BD}$.
